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Probability: An Introduction
Book Description: Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, and other key concepts and methods essential to a thorough understanding of probability. Designed for use by math or statistics departments offering a first course in probability. 360 illustrative problems with answers for half. Only high school algebra needed. Chapter bibliographies | 677.169 | 1 |
To many American high school students, calculus is a set of tools and rules that do nothing, leaving the student to never comprehend the innate beauty and powerful practicality that is calculus.
In this sequence, we set out to recapture the intuitive essence of the mathematics presented to us by Newton and Liebniz.
Sequence
The Infinitesimal™
This is the opening round of what will amaze students. The idea of the infinitesimal was borne from ancient times, and students will explore its roots and development over a period of 2000 years. Students will apply this concept to solve a range of practical mathematical problems involving areas and volumes.
In this chapter, students discover the ideas of incremental change, the derivative, and they discover that there exists a beautiful relationship between the integral and derivative. We call it... The Fundamental Theorem of Calculus.
Isaac Newton was the first scientist/mathematician to codify the ideas of the calculus. He used it solve a range of amazing physical problems, and with it he was able to show unknown mathematical relationships present in the very laws of the universe. Students will spend their time making these same discoveries.
The Calculus sequence consists of three 30-hour workshops practice problems, and concept synthesis. Academic year students are required to complete a minimal amount of practice problems.
Prerequisites
Students should have completed our Advanced Math sequence or Pre-Calculus before taking any of The Calculus courses.
CDE AP Calculus Standards
1.0 Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions.
2.0 Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.
3.0 Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value theorem.
4.0 Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability.
5.0 Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.
6.0 Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of problems in physics, chemistry, economics, and so forth.
7.0 Students compute derivatives of higher orders.
8.0 Students know and can apply Rolle's theorem, the mean value theorem, and L'Hôpital's rule.
9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
10.0 Students know Newton's method for approximating the zeros of a function. 11.0 Students use differentiation to solve optimization (maximum-minimum problems) in a variety of pure and applied contexts.
12.0 Students use differentiation to solve related rate problems in a variety of pure and applied contexts.
13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals.
14.0 Students apply the definition of the integral to model problems in physics, economics, and so forth, obtaining results in terms of integrals.
15.0 Students demonstrate knowledge and proof of the fundamental theorem of calculus and use it to interpret integrals as antiderivatives.
16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
17.0 Students compute, by hand, the integrals of a wide variety of functions by using techniques of integration, such as substitution, integration by parts, and trigonometric substitution. They can also combine these techniques when appropriate.
18.0 Students know the definitions and properties of inverse trigonometric functions and the expression of these functions as indefinite integrals.
19.0 Students compute, by hand, the integrals of rational functions by combining the techniques in standard 17.0 with the algebraic techniques of partial fractions and completing the square.
20.0 Students compute the integrals of trigonometric functions by using the techniques noted above.
21.0 Students understand the algorithms involved in Simpson's rule and Newton's method. They use calculators or computers or both to approximate integrals numerically.
22.0 Students understand improper integrals as limits of definite integrals.
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges.
24.0 Students understand and can compute the radius (interval) of the convergence of power series.
25.0 Students differentiate and integrate the terms of a power series in order to form new series from known ones.
26.0 Students calculate Taylor polynomials and Taylor series of basic functions, including the remainder term.
27.0 Students know the techniques of solution of selected elementary differential equations and their applications to a wide variety of situations, including growth-and-decay problems. | 677.169 | 1 |
NEW HEADWAY. Fourth edition. Elementary
From May Fourth to June Fourth: Fiction and Film in Twentieth-Century China
1993 | 464 | ISBN: 0674325028 , 067432501X | PDF | 23 Mb
From May Fourth to June Fourth will he warmly welcomed. It should be of great interest to all concerned with literary developments in the contemporary world on the one hand, and on the other with the enigmas surrounding China's alternating attempts to develop and to destroy herself as a civilization. - Cyril Birch University of California, Berkeley ... link between the physical world and its visualization is geometry. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. The wide range of topics includes curve theory, a detailed study of surfaces, curvature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss-Bonnet theorem. The section on cartography demonstrates the concrete importance of elementary differential geometry in applications. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study. The only prerequisites are one year of undergraduate calculus and linear algebra. | 677.169 | 1 |
Algebra 1
Algebra 1 is the second math course in high school
and will guide you through among other things expressions, systems
of equations, functions, real numbers, inequalities, exponents,
polynomials, radical and rational expressions.
This Algebra 1 math course is divided into 12
chapters and each chapter is divided into several lessons. Under
each lesson you will find theory, examples and video lessons. | 677.169 | 1 |
A provocative collection of papers containing comprehensive reviews of previous research, teaching techniques, and pointers for direction of future study. Provides both a comprehensive assessment of the latest research on mathematical problem solving, with special emphasis on its teaching, and an attempt to increase communication across the active
Systems and their mathematical description play an important role in all branches of science. This book offers an introduction to mathematical modeling techniques. It is intended for undergrad students in applied natural science, in particular earth and environmental science, environmental engineering, as well as ecology, environmental chemistry, chemical... more...
Maths Problem Solving – Year 6 is the sixth book in the Maths Problem Solving series. The books have been written for teachers to use during the numeracy lesson. They cover the ?solving problem' objectives from the numeracy framework. This book contains three chapters; Making decisions, Reasoning about numbers or shapes and Problems involving... more...
Dig into problem solving and reflect on current teaching practices with this exceptional teacher's guide. Meaningful instructional tools and methods are provided to help teachers understand each problem solving strategy and how to use it with their students. Teachers are given opportunities to practice problems themselves and reflect on how they... more...
Mathematical Applications and Modelling is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate the diversity within the theme and present research that translates into classroom pedagogies.The book,... more...
Solving Word Problems for Life, Grades 6-8 offers students who struggle with math a daily opportunity to improve their skills. The book offers 180 math word problems. The first 30 focus on 6th-grade math standards, the second 30 on 7th-grade standards, and the last 30 on 8th-grade standards. There is also a section of more difficult, extra-credit problems... more... | 677.169 | 1 |
Mathematics for Computer Graphics
This text covers all mathematical techniques needed to resolve geometric problems and design computer programs for computer graphic applications. It also discusses problem-solving techniques using vector analysis and includes a chapter on geometric algebra. | 677.169 | 1 |
Introduction to Problem Solving Grades 3-5
9780325009704
ISBN:
0325009708
Edition: 2 Pub Date: 2007 Publisher: Heinemann
Summary: Susan O'Connell is the editor of Heinemann's Math Process Standards series, as well as the author its volumes Introduction to Problem Solving (grades PreK - 2, 3 - 5, and 6 - 8) and Introduction to Communication (grades PreK - 2, 3 - 5, and 6 - 8). She also wrote the popular Now I Get It (Heinemann, 2005). Sue has a varied background, including years as a classroom teacher, a school-based instructional specialist, a ...testing coordinator, a talented-and-gifted teacher, a district school-improvement specialist, and a university professional-development schools coordinator. Currently she is a project consultant for a federal teacher-quality grant in the College of Education at the University of Maryland. Additionally, she is an educational consultant, conducts mathematics seminars for teachers throughout the country, and a Heinemann Professional Development Provider.
O'Connell, Susan is the author of Introduction to Problem Solving Grades 3-5, published 2007 under ISBN 9780325009704 and 0325009708. Twelve Introduction to Problem Solving Grades 3-5 textbooks are available for sale on ValoreBooks.com, five used from the cheapest price of $72.80, or buy new starting at $37.85 | 677.169 | 1 |
Book summary
Daniel Maki and Maynard Thompson provide a conceptual framework for the process of building and using mathematical models, illustrating the uses of mathematical and computer models in a variety of situations. This text helps students learn that model building is a dynamic process involving simplification, approximation, abstraction, analysis, computation, and comparison. Students begin the process of model building with a consideration of phenomena arising in another academic area or in the real world. [via] | 677.169 | 1 |
MQR.4.3 Functions and Their Graphs
This unit forms the core of the course. The mathematics includes reviewing functions that students have previously studied and using the functions and their graphs to analyze familiar but complex problem settings.
Instructional Days (suggested)
54 - 65 days
Click on subtopics below to see resources from the Ohio Resource Center | 677.169 | 1 |
engineering statics calculator
Personally, I've found a good calculator is invaluable for some engineering courses. The Pickett N4ES is particularly good for electrical engineering courses due to the dual base logarithmic scale (a lot of problems require base 10 logs). It also solves quadratic equations very quickly using a visual iterative process.
Of course, it doesn't help all that much in statistics, since it doesn't do sums. Then again, Microsoft Excel can do anything you want to do for statistics and most of what you want to do for any other course (provided you simplify the calculus problems by hand into something you can enter into Excel). Edit: Or, alternatively, you can buy a Picket N525-ES that's specifically designed for statistics.
I've always wondered what some of my profs would say if I showed up to class with a slide rule......
Depends on whether you can actually use all of the scales on it or not. The older ones are impressed as hell, while the younger ones barely have a clue what it is.
Of course, buying the TI-89 and not being able to figure out how to convert from rectangular coordinates to polar coordinates isn't very impressive either. I'm amazed at how many people fork out over a $100 dollars for a calculator and don't know how to use it - they don't know that most of the constants they'll need are already stored in the calculator or that they can add any additional constants that they need, they do strange things that lock up their calculator to the point they can't even turn them off, they can't find any of the functions they need, etc.
It's funny when someone comes in at the start of a class with their new, better calculator, and after a couple weeks they're using their old calculator because they don't have time to learn the new one and do their course work at the same time.
Of course, eventually they do learn how to use the calcuator they buy, but buying one on the first day of class makes for a traumatic life.
I think that if they're going to require an expensive calculator, then they ought to teach you how to use it for the things you need it for too. Otherwise, yeah, you're better off using the one you already know how to use than shelling out a bunch of money and wasting more time finding the functions on the calculator than it would take to solve the problems by hand. | 677.169 | 1 |
some textbooks, the explanations are unnecessarily long and convoluted because the publishers require them to be nice and thick because they think that it makes their prices look less ridiculous, but don't let that stop you. If you think your textbooks explanation is difficult to understand, google the concept. Having it explained in more than one way is a great way to help you understand something.
Also, I find that it helps to pretend that you're a teacher who's going to have to explain whatever they're reading about to their students the next day.
It really helps you pay attention to what you're reading when you also have to think about how you're going to have to explain it.
About the pretending you're a teacher thing, often times if I find myself dumbfounded with a concept, I'll go and try to explain it to my 8 year old niece. Works wonders. Makes me think about what the authors are trying to get across. | 677.169 | 1 |
Math
Algebra I
The basic concepts of Algebra are introduced in this full-year course. Students will use linear and quadratic equations to solve application problems from real situations. Graphs of equations will also be used in problem solving. Upon completion of the course, students will have the necessary background to be successful in their higher level mathematics courses.
Algebra II
Students who have successfully completed Algebra I are eligible for this course. Sophomores may take this course concurrently with Geometry provided they receive a recommendation from their Algebra I teacher. In this full-year course, students use problem solving and critical thinking skills to solve non-routine problems with real world applications. Students review their Algebra I skills and are introduced to new topics in algebra including rational expressions, complex numbers, quadratic equations, polynomial equations, conic sections, logarithmic functions and various topics in trigonometry. Several projects which integrate mathematics with other subjects by way of technology and other resources are required.
Integrated I
This is a full-year course which deals with Algebra as a primary subject, yet integrates all concepts of various mathematics courses and applications. The course deals with beginning Algebra techniques, up to and including graphing. In addition, problem solving is stressed along with the basic emphasis of a more conventional Algebra I course. The course is part of the VISTA program, which incorporates a grading system that allows for the extension of day and/or year in order for students to experience success. Integrated II
Students who have successfully completed Integrated Mathematics I are eligible for this course which is the sequential course in the VISTA Integrated Mathematics program. In addition to reviewing the concepts learned in Integrated Mathematics I, the students will work with radicals and radical equations, systems of equations, exponents, and polynomials. Also, a significant amount of time is spent on preparation for the HSPT, taken in the students' third year. The course follows the philosophy of the VISTA program, which offers an extended day or an extended year, if necessary, for the students to achieve success in the course.
Geometry
Students who successfully complete Algebra I or its equivalent are eligible for this course. Topics will include postulates, deductive reasoning/proofs, parallel and perpendicular lines, congruent triangles, polygons, indirect reasoning, similarity, geometry of the right triangle, circles, constructions, and logic.
Pre-Calculus
Students who have successfully completed Algebra II and Geometry are eligible for this course. Precalculus is intended to provide the mathematical background necessary for success in first-year college calculus. Topics studied include polynomial, exponential, and trigonometric functions, inequalities, analytic geometry in both polar and Cartesian coordinates, vectors, determinants, sequences, series and the fundamental concepts of limits and derivatives. The use of scientific calculators and computer software in problem solving will be stressed. Some sections of this course are Honors level and will be weighted as an Honors course.
Calculus
Students who have successfully completed Precalculus and are recommend- ed by the instructor are eligible. This full-year course introduces the fundamental concepts of Differential and Integral Calculus. Students will use derivatives and integrals to solve applications. The course is intended as a foundation for a rigorous college calculus course, not as a replacement for a college course. Students majoring in engineering and science will find this background very helpful when taking college mathematics courses. Honors sections are weighted courses.
A.P. Calculus
Students who have successfully completed Precalculus with a grade of "B" or higher and been recommended by their instructors are eligible. Equivalent to a standard first semester college calculus course, this course is intended for students planning to major in mathematics, engineering, science, or a related field. A rigorous approach is utilized in the development of major concepts and theorems throughout the course of study. Topics will include limits, continuity, techniques of differentiation, techniques of integration, applications of the derivative and integral, and logarithmic and exponential functions. Advanced Placement Calculus is weighted as a college level course.
We are a dynamic and nurturing community of learners that empowers students to reach their individual potential by
providing a creative atmosphere for innovative learning and academic excellence. | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Mathematics Through Applications
Fundamental Mathematics through Applications focuses on relevant content, motivating real-world applications, examples, and exercises demonstrating ...Show synopsisFundamental Mathematics through Applications focuses on relevant content, motivating real-world applications, examples, and exercises demonstrating how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format pairing an example with a corresponding practice exercise encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive problem set per section incorporating related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and historical connections. Compelling Historical Notes give students further evidence that mathematics grew out of a universal need to find efficient solutions to everyday problems. Plenty of practice exercises provide ample opportunity for students to thoroughly master basic mathematics skills and develop confidence in their understanding1496904Good. Paperback. May include moderately worn cover, writing,...Good. Paperback. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780321496904 | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
Master the basic concepts and methodologies of digital signal processing with this systematic introduction, without the need for an extensive mathematical background. The authors lead the reader through the fundamental mathematical principles underlying the operation of key signal processing techniques, providing simple arguments and cases rather than detailed general proofs. Coverage of practical implementation, discussion of the limitations of particular methods and plentiful MATLAB illustrations allow readers to better connect theory and practice. A focus on algorithms that are of theoretical importance or useful in real-world applications ensures that students cover material relevant to engineering practice, and equips students and practitioners alike with the basic principles necessary to apply DSP techniques to a variety of applications. Chapters include worked examples, problems and computer experiments, helping students to absorb the material they have just read. Lecture slides for all figures and solutions to the numerous problems are available to instructors | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Discrete mathematics- The mathematics of integers and of collections of object underlies the operation of digital computer, and is used widely in all fields of computer science for reasoning about data structures algorithms and complexity. The primary objective of subject is to prepare students mathematically for the study of computer engineering. Topics covered in the course include proof techniques, logic and sets, functions, relations, counting techniques, probability and recurrences.
By the end of the course, students should be able to formulate problems precisely, solve the problems, apply formal proof techniques, and explain their reasoning clearly. Illustrate by example, basic terminology and model problems in computer engineering using graphs and trees
3. Multiplexers: Application like Realization of Boolean expression using Multiplexer. 4. Demultiplexers: Applications like Realization of ROM using Demultiplexer.
5. BCD adder/Subtractor using 4 bit binary adder 7483.
6. Parity generator / detector.
B. Sequential Circuit Design
1.Flip flops, Registers and Counters (Study and Write up only).
2.4-bit Multiplier / Divider (Study and Write up only).
3.Ripple counter using flip-flops.
4.Sequence generator using JK flip-flop.
5.Sequence detector using JK flip-flop.
6.Up-down counter using JK flip-flop.
7.Modulo N counter using 7490 & 74190 (N>10).
8.Pseudo random number generator.
9.Design of a barrel shifter.
C. Study /Implement of VHDL and examples of Combinational and sequential circuits
1.Combinational Circuits: Adder, MUX
2.Sequential Circuits: Asynchronous or Synchronous Counter
D. ASM, PALS and FPGA
1.Simple ASM using multiplexer controller method.
2.Implementation of combinational logic using PLAs
3.Study of FPGA devices (Study and Write up only).
•Instructor will frame assignments based on the suggested assignments as given above. Students will submit the term work in the form of journal consisting of minimum of 16 assignments of which assignment of Group C and 2 assignments from Group D are compulsory.
•Term work assessment be done progressively and questions will be asked to judge the understanding of assignments performed.
Understand the importance of professional behaviour at the work place, Understand and Implement etiquettes in workplace, presenting oneself with finesse and making others comfortable in a business setting. Importance of first impression, Grooming, Wardrobe, Body language, Meeting etiquettes (targeted at young professionals who are just entering business environment) , Introduction to Ethics in engineering and ethical reasoning, rights and responsibilities,
UNIT IV: Interpersonal relationship (04 hours)
a) Team work, Team effectiveness, Group discussion, Decision making - Team Communication. Team, Conflict Resolution, Team Goal Setting, Team Motivation Understanding Team Development,
Team Problem Solving, Building the team dynamics. Multicultural team activity
b) Group Discussion- Preparation for a GD, Introduction and definitions of a GD, Purpose of a GD, Types of GD, Strategies in a GD , Conflict management, Do's and Don'ts in GD
UNIT V: Leadership skills (02 hours) Leaders' role, responsibilities and skill required - Understanding good Leadership behaviours, Learning the difference between Leadership and Management, Gaining insight into your Patterns, Beliefs and Rules, Defining Qualities and Strengths of leadership, Determining how well you perceive what's going on around you, interpersonal Skills and Communication Skills, Learning about Commitment and How to Move Things Forward, Making Key Decisions, Handling Your and Other People's Stress, Empowering, Motivating and Inspiring Others, Leading by example, effective feedback
UNIT VI: Other skills (02 hours)
a)Time management- The Time management matrix, apply the Pareto Principle (80/20 Rule) to time management issues, to prioritise using decision matrices, to beat the most common time wasters, how to plan ahead, how to handle interruptions , to maximise your personal effectiveness, how to say "no" to time wasters, develop your own individualised plan of action
Each class should be divided into three batches of 20-25 students each. The sessions should be activity based and should give students adequate opportunity to participate actively in each activity. Teachers and students must communicate only in English during the session. Specific details about the teaching methodology have been explained in every activity given below.
Practical Assignments (Term work)
Minimum 8 assignments are compulsory and teachers must complete them during the practical sessions within the semester. The teacher should explain the topics mentioned in the syllabus during the practical sessions followed by the actual demonstration of the exercises. . Students will submit report of their exercise (minimum 8) assignments as their term work at the end of the semester but it should be noted that the teacher should assess their assignment as soon as an activity is conducted. The continual assessment process should be followed.
1. SWOT analysis
The students should be made aware of their goals, strengths and weaknesses, attitude, moral values, self confidence, etiquettes, non-verbal skills, achievements etc. through this activity. The teacher should explain to them on how to set goals, SWOT Analysis, Confidence improvement, values, positive attitude, positive thinking and self esteem. The teacher should prepare a questionnaire which evaluate students in all the above areas and make them aware about these aspects.
2. Personal & Career Goal setting – Short term & Long term
3 Presentation Skills
Students should make a presentation on any informative topic of their choice. The topic may be technical or non-technical. The teacher should guide them on effective presentation skills. Each student should make a presentation for at least 10 minutes.
4. Letter/Application writing
Each student will write one formal letter, and one application. The teacher should teach the students how to write the letter and application. The teacher should give proper format and layouts.
5. Report writing
The teacher should teach the students how to write report .. The teacher should give proper format and layouts. Each student will write one report based on visit / project / business proposal etc.
6. Listening skills
The batch can be divided into pairs. Each pair will be given an article (any topic) by the teacher. Each pair would come on the stage and read aloud the article one by one. After reading by each pair, the other students will be asked questions on the article by the readers. Students will get marks for correct answers and also for their reading skills. This will evaluate their reading and listening skills. The teacher should give them guidelines on improving their reading and listening skills. The teacher should also give passages on various topics to students for evaluating their reading comprehension.
7. Group discussion
Each batch is divided into two groups of 12 to 14 students each. Two rounds of a GD for each group should be conducted and teacher should give them feedback.
8. Resume writing
Each student will write one formal letter, and one application. The teacher should teach the students how to write the letter and application. The teacher should give proper format and layouts.
9. Public Speaking
Any one of the following activities may be conducted :
2.Prepared speech (topics are given in advance, students get 10 minutes to prepare the speech and 5 minutes to deliver.
3.Extempore speech (students deliver speeches spontaneously for 5 minutes each on a given topic
)
4.Story telling (Each student narrates a fictional or real life story for 5 minutes each)
5.Oral review ( Each student orally presents a review on a story or a book read by them)
1.Write X86/64 Assembly language program (ALP) to add array of N hexadecimal numbers stored in the memory. Accept input from the user.
2.Write X86/64 ALP to perform non-overlapped and overlapped block transfer (with and without string specific instructions). Block containing data can be defined in the data segment.
3.Write 64 bit ALP to convert 4-digit Hex number into its equivalent BCD number and 5-digit BCD number into its equivalent HEX number. Make your program user friendly to accept the choice from user for:
(a) HEX to BCD b) BCD to HEX (c) EXIT.
Display proper strings to prompt the user while accepting the input and displaying the result. (use of 64-bit registers is expected)
4.Write X86/64 ALP for the following operations on the string entered by the user. (use of 64-bit registers is expected)
5.Write 8086 ALP to perform string manipulation. The strings to be accepted from the user is to be stored in data segment of program_l and write FAR PROCEDURES in code segment program_2 for following operations on the string:
(a) Concatenation of two strings (b) Number of occurrences of a sub-string in the given string Use PUBLIC and EXTERN directive. Create .OBJ files of both the modules and link them to create an EXE file.
6.Write X86/64 ALP to perform multiplication of two 8-bit hexadecimal numbers. Use successive addition and add and shift method. Accept input from the user. (use of 64-bit registers is expected)
7.Write 8087ALP to obtain:
i) Mean ii) Variance iii) Standard Deviation
For a given set of data elements defined in data segment. Also display result.
Group B 1. 8255
(a)Write 8086 ALP to convert an analog signal in the range of 0V to 5V to its corresponding digital signal using successive approximation ADC and dual slope ADC. Find resolution used in both the ADC's and compare the results.
(b)Write 8086 ALP to interface DAC and generate following waveforms on oscilloscope,
(d)Write 8086 ALP to print a text message on printer using Centronixs parallel printer interface. NOTE: Select any two from 8255 assignments
2. 8253
Write 8086 ALP to program 8253 in Mode 0, modify the program for hardware retriggerable Mono shot mode. Generate a square wave with a pulse of 1 ms. Comment on the difference between Hardware Triggered and software triggered strobe mode. Observe the waveform at GATE & out pin of 1C 8254 on CRO
3. 8279
Write 8086 ALP to initialize 8279 and to display characters in right entry mode. Provide also the facility to display
•Character in left entry mode.
•Rolling display.
•Flashing display
4. 8251
Perform an experiment to establish communication between two 8251 systems A and B. Program 8251 system A in asynchronous transmitter mode and 8251 system B in asynchronous receiver mode. Write an ALP to transmit the data from system A and receive the data at system B. The requirements are as follows:
Transmission:
•message is stored as ASCII characters in the memory.
•message specifies the number of characters to be transmitted as the first byte.
Reception:
•Message is retrieved and stored in the memory.
•Successful reception should be indicated.
5. 8259
Write 8086 APL to interface 8259 in cascade mode (M/S) and demonstrate execution of ISR in following manner:
Main program will display two digits up counter. When slave IRQ interrupt occurs, it clears the counter and starts up counting again. When Master IR1 interrupt occurs, it resets the counter to FFH and starts down counting.
6. TSR Program
Write a TSR program in 8086 ALP to implement Real Time Clock (RTC). Read the Real Time from CMOS chip by suitable INT and FUNCTION and display the RTC at the bottom right corner on the screen. Access the video RAM directly in your routine.
7. TSR Program
Write a TSR program in 8086 ALP to implement Screen Saver. Screen Saver should get activated if the keyboard is idle for 7 seconds. Access the video RAM directly in your routine.
Student will submit the term work in the form of Journal consisting of minimum of 13 experiments with all seven experiments from group A and any 5 assignments from group B and group C assignments. Practical examination will be based on the term work and questions will be asked to judge the understanding of assignments performed at the time of examination. | 677.169 | 1 |
As the author explains in his introduction: "This book has three intended audiences and serves three different purposes. First, it may be used as a graduate-level introduction to a fascinating area of mathematics ⋯. The second intended audience consists of professional combinatorialists, for whom this book could serve as a general reference ⋯. Finally, this book may be used by mathematicians outside combinatorics whose work requires them to solve a combinatorial problem."
The book serves all of these audiences well. The first chapter is a basic introduction to combinatorics and includes the fundamental counting formulas organized as counting functions under various conditions. The second chapter is devoted to a discussion of sieve methods. The remainder of the book consists of two long chapters: Partially ordered sets and Rational generating functions.
The book contains many careful examples and includes a large variety of exercises. The exercises are rated as to difficulty and a complete set of solutions is included. In addition each chapter contains a collection of historical notes and an extensive set of references. | 677.169 | 1 |
Kickstarter a letter by a "Donald Ross" that some people think is by Mark Twain: Things a Scotsman Wants to Know. It qualifies for the category of "inverse problems nobody will know the answer to unless someone builds a time machine".)
However, they're not diving into axing algebraic manipulation from the curriculum yet; rather Computer Based Math (abbreviated CBM) is planning to "rewrite key years of school probability and statistics from scratch". This is a reasonable first step given statistics is often taught computer based or at least calculator based these days (my colleague who teaches AP Statistics next door does so) and it does feel very silly to work through a passel of "figure out the standard deviation" problems by hand.
However, I'm going to play devil's advocate again with a thought experiment. Since algebraic manipulation is not being removed at this time, these questions aren't going to be applicable to Estonia yet, but presuming Computer Based Math continues working with them it should come up soon.
Suppose you are in a curriculum where you are used to algebraic manipulations being done by a CAS system. You are learning about statistics and come across these formulas:
What is necessary to use the formulas conceptually? What understandings might someone lack by not having experienced the algebra directly? Is it possible to understand the progressive nature and relations with these formulas just by looking at them? Is it necessary (to be well-educated in statistics) to do so? If it is necessary, what specific errors could somebody potentially make in a statistics calculation? Could this be mitigated by the text? Could this be mitigated by steps taking during the CAS portion of the education that while not leading to lengthy practice in "manipulate the algebra" problems will still allow understanding of the text above?
Is it possible to explain something too well? That is, something appears very clear to students after it is explained, so they don't practice (or at least pay attention to their practice because they assume they already understand the topic), and then the lack of practice means they forget what was explained? I'm not meaning "they never learned it in the first place" but rather "they learned it so well that they forgot it because they assumed the memory was permanent". (This is a slightly different issue than students who assume they learn something but really just keep their misconceptions.)
Are there circumstances where practice can actually lessen understanding; for example, when a student who learns a "trick" that works for an entire worksheet may attempt the same trick in circumstances where it doesn't work? Thus it may be a bad idea at times to have a student practice a topic without all the special cases? (Specific example: suppose a student practices integer addition using only a positive with a negative number, but doesn't attempting adding negative numbers with negative numbers until later. Will their earlier practice hinder their learning in the new situation?)
Each of the TED-Ed videos is meticulously animated and represents, I am sure, many many (many) hours of effort. Knowing this made the TED-Ed take on logarithms rather painful to watch:
Oof. Let me attempt to sort my thoughts:
1. The hook baffled me.
A hook should, optimally, be incorporated into the topic being learned. This hook was simply a preview of a future part of the video, and didn't carry much interest on its own. The "red eyes" made me think it was referring to the eye-bleedingly long numbers being presented.
While my own logarithm video isn't perfect (also not entirely comparable since it's about the addition property in particular) I do at least manage a hook that's useful in the explanation of the topic.
2. "…small numbers and in some cases extremely large numbers leading us to the concept of logarithms."
Logarithms come out of the inverse concept of an exponential. The numbers don't have to be large or small. (If you want to get historical, they were often used as a method to multiply quickly by turning the operation into addition.) While a logarithmic scale can be used to handle large or small numbers, I don't see how that leads to the statement in the video.
3. "the exponent p is said to be the logarithm of the number n"
Math videos often are on the glacially slow side, but this part was presented so fast parts of my brain melted.
Look: Logarithms represent, in essence, the first new mathematical operation students have had to reckon with since grade school. They cause intuitions to fail. I have seen students who have never had problems with mathematics before have them for the first time with logarithms.
It's worthwhile, then, to spend a little more than five seconds on your definition.
The definition is confusing, anyway; a logarithm is a function. It applies from one number to another number in a specific way. It is not simply an extract from an exponential equation. While the video mentions that (sort of) it waffles on the implications of introducing a new mathematical operation.
4. "…log base 10 is used so frequently in the sciences that it has the honor of having its own button."
First off, no: the sciences often use base e (given how much continuous growth and decay happens in real life). Base 10 logarithms do still get used for logarithmic scales, but the statement as given in the video is just confusing.
Also, that's a TI graphing calculator? Which one of has a logarithm button but not a natural logarithm button? Even the TI-81 has one.
5. "If the calculator will figure out logarithms for you, why study them?"
The answer the video gives … is so you can figure out a logarithm base 2.
That's a terribly weak answer, given a.) yes there are many applications of logarithms where understanding the mathematics is both good and necessary, and the video even goes into one application immediately after making this statement b.) the answer doesn't really answer the question (since it doesn't explain where the computer science-related equation came from) c.) with the current operating system, Texas Instruments calculators are perfectly capable of putting in alternate bases without a change of base formula (The video incidentally doesn't mention the change of base formula even though one of the questions in the post assessment asks what it is.) and d.) The statement presumes the use of a calculator in the first place (computer-based systems are also perfectly capable of doing logarithms with alternate bases).
6. The video then wants to show how useful logarithms are by giving a formula from science.
Based on the post-test, I'm guessing this part is here merely to show how logarithms are used in "real life".
In the master catalog of Ways to Convince Students Why Something is Useful, "look, a formula that shows up in science!" ranks somewhere between "because math is good for you" and "so you can get into a good college".
By cooperative learning tasks I mean giving particular "jobs" to students during group work; here's a sampling from this website:
Checker: Checks team members for understanding and agreement
Datakeeper: Keeps track of information generated by group
Helper: Gives help in reading, spelling, problem solving, or using materials
Questioner: Asks questions of instructor or other groups
Reporter: Gives oral reports to the total group
Summarizer: Sums up what the group did or the conclusions the group came to
Validator: Paraphrases what is said for clarity
Writer/Recorder: Writes down ideas and records the task
I tried experimenting with them last year (based on the urging of several people) but I've been distinctly unhappy. It feels like the jobs segment up the work in a rote sort of way which gives a student permission to "shut down" when they aren't needed for something in particular. I've still had some luck with engineering-like projects which involve building, but this sort of thing fails for me in general. For example, today I'm having my Algebra I students work on these questions in groups:
You have an a row by b column matrix
and want to multiply by a x row by y column matrix.
1. When is this multiplication impossible?
2. If the multiplication is possible, what is the size of the new matrix?
3. When multiplying 2×2 matrices, there is an identity operation (just like multiplying by 1 is an identity operation in arithmetic). What is it?
4. What about for nxn matrices?
5. Give an example (with all work) that shows that multiplying 2×2 matrices is in general not a commutative operation.
6. Even though the commutative law doesn't apply in general there are specific cases where it works. Give an example of a matrix A and B such that AB = BA. | 677.169 | 1 |
MathHelper is a unique application for students. The uniqueness of the application is that it allows us to see not only the answer, but a detailed solution of the problem. Now you do not need to order the work in math or ask for help from classmates - assistant in mathematics will do everything himself. In addition to solving problems, the application includes the theory on these topics and a scientific calculator.
MathHelper Lite allows you to solve a wide range of tasks. MathHelper allows you to quickly solve typical mathematical exercises of the linear and vector algebra, devided in 4 sections:
3. Vector Algebra - Vectors: *Finding the magnitude or length of a Vector *Collinearity of two Vectors *Orthogonality of vectors *Vector Addition, Subtraction and Scalar Multiplication *Vector Multiplication *Finding the Angle Between two Vectors *Finding the cosine of the angle between the vectors AB and AC *Finding the projection of one Vector on another *Coplanarity of the Vectors
4. Vector Algebra - Figures: *Calculate the area of a triangle *Whether the four points lie on one plane *Calculate the volume of a tetrahedron (pyramid) *Find the volume and height of a tetrahedron (pyramid) | 677.169 | 1 |
Ideas from Classroom Teachers for Vectors
In general, vectors seem to be a counter-intuitive subject for students, possibly because separating a force (just the magnitude and direction part) from what it acts on is abstract. One possible tie-in would be anything involving wind, which is something familiar. Also, students know of translations and rotations from geometry, so invoking those transformations would help with the familiarity aspect.
Emphasize that a vector is defined by its direction and magnitude, not by its location.
To be considered: the zero vector; unit vector; vectors in terms of i and j; horizontal and vertical components of a vector; properties of vectors.
Students could use vectors to prove geometric statements, such as "the lines that join one vertex of a parallelogram to the midpoints of the opposite sides trisect the diagonal."
The angle between vectors can be found (proven) using the Law of Cosines and the dot product.
Wherever possible, tie vectors in with geometric transformations. For example, students already know what translations are; now they have the tools to formalize them.
Parametrics take a long time to introduce because students have been indoctrinated in x-y thinking since day one. Standard introductions to parametrics consist of some variant on the Ferris wheel problem, in which the x-coordinate and y-coordinate can both be visualized as directly dependent on time. One aspect of the Ferris wheel that needs to be brought out (even emphasized) is that by a set of parametric equations you can get a graph (in this case, a circle) which you cannot get by having a single y-in-terms-of-x function. Also (equally important) is that such a graph gets drawn in a way that represents the actual motion involved. In other words, it is usual to emphasize how to turn a pair of parametric equations into a single y = f(x), but that misses the point.
Technology note: Most graphing calculators have a "parametric mode" that allows students to investigate parametric equations graphically.
I would suggest teaching parametric equations as a separate mini-unit, perhaps just after polar coordinates (another alternative mode of graphing) and before vectors. | 677.169 | 1 |
entity and Inverse Matrices
This may, in fact, be two days masquerading as one—it depends on the class. They can work through the sheet on their own, but as you are circulating and helping, make sure they are really reading it, and getting the point! As I said earlier, they need to know that [I][I] is defined by the property AI=IA=AAIIAA, and to see how that definition leads to the diagonal row of 1s. They need to know that A-1A-1 is defined by the property AA−1=A1AA1A1=I=I, and to see how they can find the inverse of a matrix directly from this definition. That may all be too much for one day.
I also always mention that only a square matrix can have an [I][I]. The reason is that the definition requires II to work commutatively: AIAI and IAIA both have to give AA. You can play around very quickly to find that a 2×323 matrix cannot possibly have an [I][I] with this requirement. And of course, a non-square matrix has no inverse, since it has no [I][I] and the inverse is defined in terms of [I][I] | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
This book is an introduction to MATLAB and an introduction to numerical methods. It is written for students of engineering, applied mathematics, and science. The primary objective of numerical methods is to obtain approximate solutions to problems that are not obtainable by other means. This book teaches how the core techniques of numerical methods are used to solve otherwise unsolvable problems of modern technological significance.
The outstanding pedagogical features of this book are:
use of numerical experiments as a means of learning why numerical methods work and how they fail
a separate chapter reviewing the basics of applied linear algebra, and how computations involving matrices and vectors are naturally expressed in MATLAB
use of a range of examples from those that provide a succinct illustration of a basic algorithm, to those that develop solutions to substantial problems in engineering
consistent use of well-documented and structured code written in the MATLAB idiom
a library of general purpose routines—the NMM Toolbox—that are readily applied to new problems
a progressive approach to algorithm development leading the reader to an understanding of the more sophisticated routines in the built-in MATLAB toolbox.
The primary goals of the book are to provide a solid foundation in applied computing, and to demonstrate the implementation and application of standard numerical methods to practical problems. This is achieved by a systematic development of techniques beginning with the simple and ending with the sophisticated. Good programming practice is used throughout to show the reader how to clearly express and document computational ideas. By providing an extensive library of working codes, as well as an exposition of the methods used by the built-in MATLAB toolbox, the reader is challenged by the application of numerical methods to practical problems. This bypasses the ritual of forcing the reader to reinvent simple programs that fail on more technologically significant, practical problems Ingram Pearson | 677.169 | 1 |
The concept of (Functions and functional tables) is explained by expert tutors at TCYonline.com which is an authority in online tutoring in Math and homework help... More...
The concept of (Functions and functional tables) is explained by expert tutors at TCYonline.com which is an authority in online tutoring in Math and homework help to students from K-12. We also prepare students for SAT, GRE, GMAT, ACT and various state level exams like FCAT, ISAT, CAHSEE and many more. Please visit for more exciting videos, Free math worksheets, state assessment tests, games, puzzles and free trial session on any topic in Math Functions
Skill: F.8.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade )
Skill: F-IF.1. outpu | 677.169 | 1 |
This concise "Teach Yourself" text provides a thorough, practical grounding in the fundamental principles of trigonometry, which any reader can apply to his or her own field. Trigonometry Teach Yourself explores the use of calculators and contains worked examples and exercises (with answers) within each chapter.
Trigonometry Teach Yourself is suitable for beginners, but it also goes beyond the basics to offer comprehensive coverage of more advanced topics. Each chapter features numerous worked examples and many carefully graded exercises, and full demonstrations of trigonometric proofs are given in the answer key.
About author :
McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide.
This concise "Teach Yourself" text provides a thorough, practical grounding in the fundamental principles of trigonometry, which any reader can apply to his or her own field. The text explores the use of calculators and contains worked examples and exercises (with answers) within each chapter. | 677.169 | 1 |
Book summary
The first edition of this book sold more than 100,000 copiesand this new edition will show you why! Schaums Outline of Discrete Mathematics shows you step by step how to solve the kind of problems youre going to find on your exams. And this new edition features all the latest applications of discrete mathematics to computer science! This guide can be used as a supplement, to reinforce and strengthen the work you do with your class text. (It works well with virtually any discrete mathematics textbook.) But it is so comprehensive that it can even be used alone as a text in discrete mathematics or as independent study tool! [via]
New books: 1 - 5 of 23
Softcover, ISBN 0070380457 Publisher: McGraw-Hill, 1997 2nd | 677.169 | 1 |
Algebra : Introductory and Intermediate - 4th edition
Summary: With all the support of the renowned Aufmann approach, this popular combination text helps your students prepare to master college algebra and to apply algebra in the real world.
New! Bulleted annotations have been added to the solution steps of Examples and to the You Try It solutions in the appendix, further enhancing the Aufmann Interactive Method.
New! Examples have been clearly labeled How To, ...show moreallowing students to more easily refer back to solution steps when completing corresponding exercises.
Updated! The Chapter Summary has been reformatted to include an example column, offering students the additional support of an algebraic representation of concepts, rules and definitions.
Updated! In response to instructor feedback, the number of Chapter Review Exercises and Cumulative Review Exercises has increased.
Updated! More operation application problems integrated into the Applying the Concepts exercises encourage students to judge which operation (adding, subtracting, multiplying, dividing) is needed to solve a word problem.
New! Integrating Technology (formerly Calculator Notes) margin notes provide suggestions for using a calculator in certain situations. For added support and quick reference, a scientific calculator screen is displayed on the inside back cover of the text.
New! Objective-based Worksheets accompany every section in the book for extra classroom practice or homework. These worksheets are found on the ClassPrep CD and Online Teaching Center.
Aufmann Interactive Method (AIM) encourages students to try the math as it is presented. Every section objective contains one or more sets of matched-pair examples. The first example is completely worked out; the second example, called 'You Try It,' is for the student to work. Complete worked-out solutions to these examples in an appendix enable students to check their solutions and obtain immediate reinforcement of the concept.
Integrated, easy-to-navigate learning system organized by objectives guides students with a consistent, predictable framework. Each chapter opens with a list of learning objectives, which are woven throughout the text and integrated with the print and multimedia ancillaries.
The AIM for Success Student Preface guides students in making the most of the text's features. Study Tip margin notes throughout the text refer students back to the Student Preface for advice.
Prep Tests at the beginning of each chapter help students prepare for the upcoming material by testing them on prerequisite material learned in preceding chapters. The answers to these questions can be found in the Answer Appendix, along with a reference to the objective from which the question was taken. The Go Figure problem that follows the Prep Test is a challenge problem for interested students.
Extensive use of applications that use real source data shows students the value of mathematics as a real-life tool.
Focus on Problem Solving section at the end of each chapter introduces students to various problem-solving strategies. Students are encouraged to write their own strategies and draw diagrams in order to find solutions.
Unique Verbal/Mathematical connection simultaneously introduces a verbal phrase with a mathematical operation, followed by exercises that require students to make a connection between a phrase and a mathematical process.
Projects and Group Activities at the end of each chapter offer ideas for cooperative learning.
Unique Instructor's Annotated Edition features a format rich with new instructor support materials, which are provided at point-of-use in the margins surrounding reduced student pages | 677.169 | 1 |
You should now have a clear understanding of the twelve basic function families explored in this investigation. Think of all the things that you just learned about the practical applications of mathematics. What would our world be like without various functions, each filling a unique roll in our society? | 677.169 | 1 |
When considering a mathematical theorem one ought not only to know how to prove it but also why and whether any given conditions are necessary. All too often little attention is paid to to this side of the theory and in writing this account of the theory of real functions the authors hope to rectify matters. They have put the classical theory of real functions in a modern setting and in so doing have made the mathematical reasoning rigorous and explored the theory in much greater depth than is customary. The subject matter is essentially the same as that of ordinary calculus course and the techniques used are elementary (no topology, measure theory or functional analysis). Thus anyone who is acquainted with elementary calculus and wishes to deepen their knowledge should read this. | 677.169 | 1 |
Short description Key Stage 3 (KS3) maths eBooks comprise three principle sections. These are, notably: (Read more) maths eBooks are produced such as that as well as a Publications Guide, and three principle publications corresponding to the principle sections (Number and Algebra, Geometry and Measures and Handling Data) there are individual modules produced within each principle section which are published as eBooks.
Transformations is a module within the Geometry and Measures principle section our Key Stage 3 (KS3) publications. It is one module out of a total of six modules in that principle section, the others being: • 2D Shapes and 3D Solids • Loci, Constructions and 3D Co-ordinates • Angles, Bearings and Scale Drawings • Pythagoras' Theorem, Trigonometry and Similarity • Measures and Measurements (Less) | 677.169 | 1 |
Help With Math Problems
Help With Math Problems
Friends math is a very vast subject and it plays an important role in our daily life.
It is the study
of space, relation, structure, change, and many other topics of pattern.
It becomes an essential part in all...
[More]
Help With Math Problems
Friends math is a very vast subject and it plays an important role in our daily life.
It is the study
of space, relation, structure, change, and many other topics of pattern.
It becomes an essential part in all the areas which includes engineering, social science,
medicine, natural science etc.
Calculus is one of the most important part of mathematics.
So today we are going to study
about the calculus and how to take help with math solvers to solve our math problems.
Calculus is the most important, interesting and most complicated topic in the world of
mathematics, as various online calculus tutors are available to remove its complex nature and
solve our calculus problems.
Calculus plays an important role not only in the area of maths but also in other areas like
physics, economics etc.
Calculus is basically a branch of mathematics focused on limits, functions, derivatives,
integrals, and infinite series.
Basically it is the study of Rates of Change . | 677.169 | 1 |
For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, theThis best-selling guide--which has sold more than 340,000 copies since its first publication--has been thoroughly updated throughout to correspons to current advanced calculus courses. A complete and comprehensive review of the subject, this updated edition features important new chapters on topology and Laplace transforms and essential new theorems,... more...
Large IT organizations increasingly face the challenge of integrating various web services, applications, and other technologies into a single network. The solution to finding a meaningful large-scale architecture that is capable of spanning a global enterprise appears to have been met in ESB, or Enterprise Service Bus. Rather than conform to the... more...
Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting | 677.169 | 1 |
Concept Explanations, Sample Problems, Must-Know Shortcuts.
Topics
Introduction to Matrices
Some functions are not easily written as a formula. On a graph, a step function looks like a flight of stairs. The graphs of step functions have lines with an open circle on one end and a closed circle on the other to indicate inclusion, like number line inequality graphs. A rounding step function tells us to round a decimal number to the next whole integer or the previous whole integer.
Study Your Way
Easy Help. Fun Teachers.
Expert teachers who know their stuff bring personality & fun to every video. | 677.169 | 1 |
How To Teach with DWFK Precalculus
Chapter 5: Analytic Trigonometry
This is a very important chapter for those who wish to pursue college mathematics, but not just because of the trigonometric material. The importance of equivalent expressions, the emphasis on proof, and the positive reinforcement gained from the ability to switch representations — all so important in analytic trigonometry — come as close to anything in the high school curriculum to approximating what matters to the real practitioners of mathematics. For this reason, we place deliberate emphasis on trigonometric identities as mathematical proofs and motivate them as such in the text.
Also, because their proofs are as important as their applications, we have placed the Law of Sines and the Law of Cosines in this section, along with the triangle area formulas.
Section 5.1 Fundamental Identities
Objectives
You will be able to justify the fundamental identities and use them to simplify trigonometric expressions. You will be able to use them to solve certain trigonometric equations.
Key Ideas
Cofunction identities
Odd-even identities
Domain of validity
Pythagorean identities
Identity
Trigonometric equation
Study Tips
The identities that follow directly from the triangle ratios or from the unit circle are called the Fundamental Identities. (Note that we define the concept of "identity" at the beginning of the chapter.) Eventually, you will need to memorize some identities whether they understand them or not; however, they should all be able to understand the Fundamental Identities.
Technology Tips
Graphing both sides of an identity to see if the graphs match can be a little tedious, but it is a nice way for you to verify their answers. Several other technology tips are shown in the section. Realistically, this section could be taught quite comfortably with no technology at all. Top
Section 5.2 Proving Trigonometric Identities
Objectives
You will be able to decide whether an equation is an identity and will be able to prove identities analytically.
Key Ideas
Proof of an identity
Word ladder
Study Tips
Some people have lamented the decreased emphasis on proofs in the curriculum since the advent of certain education reforms, but it is only certain kinds of proofs that have been de-emphasized. Axiomatic algebra proofs (characteristic of the "New Math" of the 60's) have been de-emphasized because they did not contribute to student understanding, and two-column proofs in geometry were de-emphasized because they gave a misleading idea of what mathematical proofs look like. Really, trigonometric identities are the ideal introduction to proofs for beginners, as they actually read like proofs in higher mathematics courses. They have a structure that beginners can understand, and you can actually produce them on your own. This textbook embraces identity proofs as pedagogically important and teaches them as such.
For example, this kind of identity verification is never suggested:
Identity:
"Proof":
Sometimes this sort of a thing is followed by a check sign, but it does not render any more educationally acceptable a mode of proof that begins with assuming what was to be proved and ends with a tautology. (We demonstrate a preferable alternative to this approach in Example 5.) Our emphasis is on constructing a logical path from what is known to what must be shown (as in the word ladders at the start of the section), as this is what mathematical proofs really look like.
Technology Tips
The main use of technology in this section is to provide graphical support for what is an identity and graphical refutation of what is not. You will not need to do this for all identities we ask them to prove. In particular, exercises 7–47 are true identities, and all that we require are the proofs.
Section 5.3 Sum and Difference Identities
Objectives
You will understand the derivations of, and be able to apply, the formulas for the cosine, sine, and tangent of a difference or sum.
Key Ideas
Angle sum formula
Reduction formula
Study Tips
There is some debate about whether modern precalculus students need to memorize these (and other) formulas or not. The debate is not about whether students should memorize things, but rather about what they should be required to memorize and why. (These formulas can be stored on their calculators.) Regardless of where one stands on this debate, precalculus students ought to see how these formulas are derived. Moreover, calculus students will use these formulas later, and it saves time if one does not have to scroll down a calculator screen to find them.
Technology Tips
Most teachers realize that you can store these (and other) formulas on your graphing calculators, either as text screens or embedded in programs. At first glance you might think that this capability gives you an advantage on tests, but you need to consider that teachers are now less inclined to award ten points on an exam for simply stating a formula. A side effect of technology is that students and teachers alike are faced with finding more creative incentives for memorization. Top
Section 5.4 Multiple-Angle Identities
Objectives
You will understand the derivations of, and be able to apply, the double-angle, half-angle, and power reducing identities.
Study Tips
The comments in the previous section about memorization apply equally well here. You will definitely use these formulas in calculus, especially the power-reducing formulas, which are the keys to finding certain antiderivatives.
Technology Tips
The trigonometric equations found in this section are intended as applications of the identities in the section, so solving them with calculators defeats their purpose. The instructions in the exercises should be carefully followed. Top
Section 5.5 The Law of Sines
Objectives
You will be able to understand the proof of the Law of Sines and will be able to use the formula to solve a variety of problems.
Key Ideas
Law of Sines
Solving Triangles
Study Tips
The Law of Sines could equally well have appeared in the previous chapter, but we felt that it deserved to be among the identities. As with the other identities in this section, the derivation of the formula is a very good thing for precalculus students to see.
Technology Tips
Application problems of the kind featured in this section have always been part of a trigonometry course, but today's students can arrive at actual answers far more quickly (and more accurately!) than students of previous generations, thanks to technology. This is a good thing, as it allows you to concentrate on the formula rather than on the grubbiness of the computations. The main use of the calculator in this section is actually as a machine that calculates. As they say, go figure. Top
Section 5.6 The Law of Cosines
Objectives
You will be able to understand the proof of the Law of Cosines and will be able to use the formula to solve a variety of problems. You will know Heron's formula and be able to use it to find areas of triangles and to solve appropriate application problems.
Key Ideas
Dihedral angle
Heron's formula
Law of Cosines
Study Tips
You ought to be able to follow the proof of the Law of Cosines, although the proof of Herons' formula might be a little heavy for some. (It's not that complicated, just a little intimidating with those five variables being pushed around.)
Technology Tips
If you are a good trigonometry student who likes to write calculator programs, you might enjoy the challenge of writing a calculator program that will solve triangles, using the Law of Sines and the Law of Cosines. The user would input three parts of a triangle (SSS or ASA or AAS) and the program would announce all six parts, having computed the missing ones by applying one of the laws. Let alone the difficulty of the programming, there are some subtle difficulties in the mathematics that make it hard to come up with a program that is correct in all cases. Good programmers should try to make the program "idiot-proof," i.e., designed to recognize and reject input values that will not determine a triangle (angles that sum to more than 180°, side lengths that do not satisfy the triangle inequality, etc.). | 677.169 | 1 |
Precalculus
9780471756842
ISBN:
0471756849
Pub Date: 2010 Publisher: Wiley
Summary: This title offers a clear writing style that helps reduce any maths anxiety readers may have while developing their problem-solving skills. It incorporates parallel word and math boxes that provide detailed annotations which follow a multi-modal approach.
Young, Cynthia Y. is the author of Precalculus, published 2010 under ISBN 9780471756842 and 0471756849. Four hundred sixty three Precalculus textbooks are ...available for sale on ValoreBooks.com, one hundred fourteen used from the cheapest price of $59.05, or buy new starting at $113 Marks in pencil, covers scuffed/scratched, minimal shelf wear, Item is intact, but may show shel... [more] MarksMarks in pencil, covers scuffed/scratched, minimal shelf wear, Item is intact, but may show shelf wear. Pages may include notes and highlighting. May or may not include suppl [more]
Marks marked/wavy due to contact with moisture/coffee | 677.169 | 1 |
Discrete Math Track
Track Content
Welcome to the Discrete Math refresher course.
This refresher is designed to refresh (or create afresh) your intuition
about the basic tools of discrete math and graph theory.
We expect to cover the bread and butter of discrete mathematics,
while also reserving time to discuss a few active research questions
in our brief tour through the territory.
In the end, you should find yourself with a deepened understanding of
combinatorics, sorting,
graph theory fundamentals, breadth- and depth-first search,
minimum spanning trees, flow algorithms,
complexity theory and notation,
approximation algorithms,
and current research areas in discrete math and graph theory.
We take the view that algorithms and analysis are easiest to internalize
when coupled with applications,
and approach each new technique with an example firmly in mind.
We will not shy away from proofs, but will do our best to
nurture the novice while exerting the expert. | 677.169 | 1 |
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BEGINNING AND INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS, shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master algebraic concepts, problem solving, and communication skills. Students develop sound mathematical skills by learning how to solve problems generated from realistic applications, instead of learning techniques without conceptual understanding. Authors Mark Clark and Cynthia Anfinson have developed several key ideas to make concepts real and vivid for students. First, the authors place an emphasis on developing strong algebra skills that support theMore... applications, enhancing student comprehension and developing their problem solving abilities. Second, applications are integrated throughout, drawing on realistic and numerically appropriate data to show students how to apply math and to understand why they need to know it. These applications require students to think critically and develop the skills needed to explain and think about the meaning of their answers. Third, important concepts are developed as students progress through the course and overlapping elementary and intermediate content in kept to a minimum. Chapter 8 sets the stage for the intermediate material where students explore the "eyeball best-fit" approach to modeling and understand the importance of graphs and graphing including graphing by hand. Fourth, Mark and Cynthia's approach prepares students for a range of courses including college algebra and statistics. In short, BEGINNING AND INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS develops strong mathematical skills using an engaging, application-driven and problem solving-focused approach to algebra | 677.169 | 1 |
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Annotations for GED Mathematics
Baker & Taylor Offers general information about what to expect on the GED test and how to prepare for it, as well as covering mathematics topics such as arithmetic, charts and graphs, probability, statistics, algebra, and geometry.
---------------------- Video Aided Instruction "Once you've mastered the algebra, geometry, and coordinate geometry topics covered in ""Pre-GED Mathematics"",."
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Solving Equations Graphic Organizer with Example
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I use this with my students in Algebra. I make a foldable with them and instruct them to fill in the steps, and then we do an example to illustrate the steps with them. They have their own foldable on hand with them all the time. I typed it up so that I could turn it into a poster sized sheet, laminate it, and refer to the poster when doing examples. I love this tool, and it works well with Max Thompson's learning focused strategies, which my school has adopted.
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$7124*ACP FUND. OF ALGEBRAIC MODELING 2E
Fundamentals of Algebraic Modeling
Fundamentals of Algebraic Modeling : An Introduction to Mathematical Modeling with Algebra and Statistics
Fundamentals of Algebraic Modeling: An Introduction to Mathematical Modeling with Algebra and Statistics
Student Solutions Manual for Timmons/Johnson/McCook's Fundamentals of Algebraic Modeling: An Introduction to Mathematical Modeling with Algebra and Statistics, 5th
Summary
FUNDAMENTALS OF ALGEBRAIC MODELING 5e presents Algebraic concepts in non-threatening, easy-to-understand language and numerous step-by-step examples to illustrate ideas. This text aims to help you relate math skills to your daily as well as a variety of professions including music, art, history, criminal justice, engineering, accounting, welding and many others.
Table of Contents
A Review of Algebra Fundamentals
Mathematical Models
Real Numbers and Mathematical Equations
Solving Linear Equations
Formulas
Ratio and Proportion
Percents
Word Problem Strategies
Graphing
Rectangular Coordinate System
Graphing Linear Equations
Slope
Writing Equations of Lines
Applications and Uses of Graphs
Functions
Functions
Using Function Notation
Linear Functions as Models
Direct and Inverse Variation
Quadratic Functions and Power Functions as Models
Exponential Functions as Models
Mathematical Models in Consumer Math
Mathematical Models in the Business World
Mathematical Models in Banking
Mathematical Models in Consumer Credit
Mathematical Models in Purchasing an Automobile
Mathematical Models in Purchasing a Home
Mathematical Models in Insurance Options and Rates
Mathematical Models in Stocks, Mutual Funds, and Bonds
Mathematical Models in Personal Income
Additional Applications of Algebraic Modeling
Models and Patterns in Plane Geometry
Models and Patterns in Right Triangles
Models and Patterns in Art and Architecture: Perspective and Symmetry
Models and Patterns in Art, Architecture, and Nature: Scale and Proportion | 677.169 | 1 |
...I have been using it professionally for years, because it is one of the math subjects that connects fully to the physical world we live in. That makes calculus very intuitive and easy to explain. What makes calculus difficult is that it requires strong math skills in foundational math up to the level of trigonometry, and any holes or weaknesses in those areas need to be addressed.
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(see
) of modules designed to make physics
concepts accessible to blind students. The collection is intended to supplement but not to
replace the textbook in an introductory course in high school or college
physics.
This module explains vector multiplication in a format that is accessible to
blind students.
Prerequisites
In addition to an Internet connection and a browser, you will need the
following tools (as a minimum) to work through the exercises in these modules:
Dot product, inner
product, or scalar product
I will begin with some background information on the dot product of two
vectors.
Background
The terms dot product, inner product, and scalar product all mean the same
thing and are used in various context's by different authors.
The term
dot product
derives from the fact that a vector product of
this sort is often written as the names of the two vectors separated by a dot.
However, that special dot character is probably not compatible with your Braille
display. Therefore, I will write the dot product of the vectors named A and B as
(A dot B)
The term scalar product derives from the fact that a vector product of this
sort more closely resembles scalar arithmetic than vector arithmetic. In
particular, unlike the cross product (that will be discussed later), the result of
the dot product does not have a direction.
Create a vector diagram on your graph board
In order for you to better understand the nature of a vector dot product, I recommend
that you create a Cartesian coordinate system on your graph board, and draw the
followingReferences to the vector coordinates
I will refer to the coordinates at the tip of vector A as ax and ay.
Similarly, I will refer to the coordinates at the tip of vector B as bx and by.
The dot product
Using this nomenclature
, the dot
product of any two vectors is given by
(A dot B) = (ax * bx) + (ay * by)
where
(A dot B) represents the dot product of the vectors named A and B
ax, ay, bx, and by are the coordinates of the tips of the vectors named
A and B respectively
So what?
By now you are probably saying "So what? Why should I care?"
Although it isn't obvious from what you see above, the dot product
of two vectors is also equal to the product of their magnitudes and
the cosine of the angle between them. In other words,
(A dot B) = Amag*Bmag*cosine(angle between A and B)
where
Amag is the magnitude of vector A
Bmag is the magnitude of vector B
The projection of A onto B
If you divide the dot product of A and B by the magnitude of B, the result is
equal to the projection of vector A onto
vector B. In other words,
(A dot B)/(Bmag) = projection of A onto B
This sort of projection operation is an operation that occurs frequently in physics.
For example, the horizontal component of a velocity vector is the projection of
the velocity vector onto the horizontal axis. Similarly, the vertical component
of a velocity vector is the projection of the velocity vector onto the vertical
axis.
Let's work through some numbers
Substituting your coordinate values into the
expression given
above
yields
(A dot B) = (ax * bx) + (ay * by), or
(A dot B) = (1.0*2.9) + (1.73*0.78), or
(A dot B) = 4.2494
We will make use of this value a little later in this module.
Compute the projection
Suppose your problem calls for the projection of vector A onto vector B. Let's
compute the value of that projection. For this,
we need to know the magnitude of vector B, which we can compute using the
Pythagorean theorem:
Bmag = sqrt(2.9*2.9 + 0.78*0.78), or
Bmag = 3.0
The projection of A onto B is equal to
Projection = (A dot B)/Bmag, or
Projection = 4.294/3 = 1.43
We will also have more to say about this value a little later in this module.
What do we mean by the projection?
Using the vectors on your graph board, draw a line segment beginning at the tip of vector A.
Make that line perpendicular to vector B and mark the point on vector B where
that line intersects vector B.
The distance from the origin to that point is the value of the projection of vector A onto vector B.
According to the above
arithmetic, that distance should be equal to 1.43 units. Hopefully when you
measure it on your graph board, you will get approximately the same value.
Compute the angle between the vectors
Suppose instead that your problem calls for the angle between the two
vectors. Given that the dot product is equal to the product of the magnitudes and the
cosine of the angle between the vectors, the cosine of the angle between the
vectors is equal to
cosine(angle) = (A dot B)/(Amag *Bmag)
You may or may not know this from your earlier experience with trigonometry, but the angle
in the above expression is the arccosine of the cosine value.
To compute the angle, we first need to compute the magnitude of vector A.
Once again using the Pythagorean theorem,
Amag = sqrt(1.0*1.0+1.73*1.73), or
Amag = 2
Now compute the angle between the vectors
We now have all of the information that we need to computer the angle between
the vectors. Using Google calculator nomenclature,
Angle = arccos((A dot B)/(Amag *Bmag)) in degrees, or
angle = arccos(4.294/(2*3)) in degrees, or
angle = 44.30 degrees
(Actually, I chose the original values in hopes of causing this final answer to
come out to 45 degrees, but the round off errors along the way threw things off
a bit.)
What have we learned?
For these two vectors, we have learned that
The angle between them is 44.3 degrees
The projection of vector A onto vector B is equal to 1.43 units 90 degrees, the cosine of the angle approaches 0, and
the dot product of the vectors approaches 0.
As the angle approaches 0 degrees, the cosine of the angle approaches 1.0 and
the dot product approaches a value that is the product of the magnitudes of the
two vectors.
For a given pair of vectors, the dot product can be thought of as a
measure of the extent to which they are parallel. The closer they are to
parallel, the greater will be the value of the dot product.
A check on the projection value
We can check our earlier projection value from a different viewpoint now that we
know the angle between the vectors.
From the drawing on your graph board, you
should see that vector A forms the hypotenuse of a right triangle and the
projection of vector A onto vector B forms the base of that triangle. You should
know from the earlier module on trigonometry that the length of the base is
base = Amag * cos(angle), or
base = 2 * cos(44.3 degrees), or
base = 1.43 units
which matches the length of the projection that we computed earlier.
Summary for vector dot product
Given two vectors, A and B with their tails at the origin and
their tips at ax, ay, bx, and by respectively
(A dot B) = (ax * bx) + (ay * by)
where
(A dot B) represents the dot product of the vectors
named A and B
also
(A dot B) = Amag*Bmag*cosine(angle between A and B)
where
Amag is the magnitude of vector A
Bmag is the magnitude of vector B
The projection of A onto B = (A dot B)/(Bmag)
The angle between A and B = arccos((A dot B)/(Amag *Bmag))
For a given pair of vectors, the dot product can be thought
of as a measure of the extent to which they are parallel.
The closer they are to parallel, the greater will be the
value of the dot product.
Cross product
Let's begin our discussion of the vector cross product with some background
information.
Background
The
cross product
, sometimes called a
vector product
, is an operation on two vectors in three-dimensional space. The operation results in a vector
that is perpendicular to both of the vectors being multiplied.
The name of the operation
The name "cross product" derives from the fact that a special
character that looks like
an "x" is often used to indicate the nature of the operation.
I doubt that the special character will display properly on your Braille
display. In this module, therefore, I will use an actual "x" character instead of the special character that is
typically used. For example, I will indicate the cross product between vectors A
and B as
AxB
A cross product with a zero result
If either of the vectors being multiplied has a magnitude of 0, the cross
product will be zero. Also if the vectors being multiplied are parallel, their
cross product will be zero.
The area of a parallelogram
Except for the case of perpendicular vectors, the magnitude of the cross product
between two vectors equals the area of a parallelogram with the vectors
forming two sides of the parallelogram.
For the case of perpendicular vectors, the parallelogram becomes a rectangle and
the magnitude of the product is the area of that rectangle.
The direction of the resultant vector
As mentioned earlier, the result of the cross product is a vector that is
perpendicular to both of the vectors being multiplied. The resultant vector can
satisfy that requirement and point in ether of two directions. The actual
direction depends on certain orientation conventions as described by the
right-hand rule
.
The right-hand rule
For a "right-handed" coordinate system, the direction of the resultant vector
for AxB can be determined as follows:
Point the forefinger of the right hand in the direction of A and point the
second finger in the direction of B. The thumb will then point in the direction
of the resultant vector.
The cross product is not commutative
If you think about this, you should realize that the cross product is not
commutative. That is to say that AxB is not the same as BxA because the
direction of the resultant vector would not be the same.
Create a vector
diagram on your graph board
Once again, in order for you to better understand the nature of a vector
cross product, I recommend that you create a Cartesian coordinate system on your
graph board, and draw the followingThe cross product
The cross product,
AxB is defined as
AxB = Amag*Bmag*sin(angle)
where
Amag is the magnitude of the vector A
Bmag is the magnitude of the vector B
angle is the angle between the two vectors, which must be less than or
equal to180 degrees
The area of the parallelogram
Use the vectors that you have drawn on your graph board to construct a
parallelogram and see if you can estimate the area of that parallelogram.
Even if you were a sighted student having the parallelogram drawn
on high-quality graph paper, it would be something of a chore to manually
determine the area of the parallelogram.
Let's work through some numbers
Let's use the cross product to determine the area of the parallelogram.
Given the
definition
of the cross product,
we see that there are three values that we need:
Amag
Bmag
angle
Same vectors as before
If we were starting out with two new vectors, we could compute the magnitude
of each vector using the Pythagorean theorem. We could also determine the angle
by computing the vector dot product that I explained earlier in this
module.
As you may have noticed, these are the same two vectors that we used earlier,
and we computed those three values earlier. Going back and recovering those
three values, we have
Amag = 2.0
Bmag = 3.0
angle = 45 degrees (at least that is what I intended for it to be)
The area of the parallelogram
Using the earlier
definition
and the
nomenclature for the Google calculator,
AxB = Amag*Bmag*sin(angle), or
AxB = 2.0*3.0*sin(45 degrees), or
AxB = 4.24 square units
The direction of the
resultant vector
If you place the end of your thumb at the origin of your Cartesian coordinate
system, you should be able, with reasonable comfort, to point your forefinger in
the direction of A and your second finger in the direction of B.
According to the
right-hand rule
, this
means that the direction of the resultant vector is the direction that your thumb is
pointing, or straight down into the graph board. 0 degrees, the sine of the angle approaches 0, and
the cross product of the vectors approaches 0.
As the angle approaches 90 degrees, the sine of the angle approaches 1.0 and
the cross product approaches a value that is the product of the magnitudes of
the two vectors.
Thus, for a given pair of vectors, the cross product can be thought of as a
measure of the extent to which they are perpendicular to one another. The closer
they are to perpendicular, the greater will be the value of the cross product.
Hence, the dot product is a measure of the extent to which two vectors are
parallel to one another, while the cross product is a measure of the extent to
which two vectors are perpendicular to one another.
Summary for vector cross product
Given two vectors, A and B with their tails at the origin
AxB = Amag*Bmag*sin(angle between A and B)
where
AxB represents the cross product of the vectors
named A and B
Amag is the magnitude of vector A
Bmag is the magnitude of vector B
The cross product is a vector operation. The resultant vector
is perpendicular to the two vectors being multiplied. The
direction of the resultant vector can be determined by the
right-hand rule.
The magnitude of the product equals the area of a
parallelogram with the vectors forming two sides of the
parallelogram.
The cross product is not commutative. In other words, AxB
is not equal to BxA.
For a given pair of vectors, the cross product can be
thought of as a measure of the extent to which they are
perpendicular to one another. The closer they are to
perpendicular, the greater will be the value of the
cross product.
Repeat the computations
I encourage you to repeat the computations that I have presented in this
lesson to confirm that you get the same results. Then do similar
computations for pairs of different vectors. For example, swap the positions
of vectors A and B and see what this does to the direction of the resultant
vector for a cross product.
Resources
I will publish a module containing consolidated links to resources on my
Connexions web page and will update and add to the list as additional modules
in this collection are published.
Miscellaneous
This section contains a variety of miscellaneous information.
Note:
Housekeeping material
Module name: Vector Multiplication for Blind Students
File: Phy1310.htm
Keywords:
physics
accessible
accessibility
blind
graph board
protractor
screen reader
refreshable Braille display
JavaScript
trigonometry
dot product
inner product
scalar product
cross product
vector product
projection by you, and collections
saved in 'My Favorites' can remember the last module you were on. You need an account
to use 'My Favorites'. | 677.169 | 1 |
0071445226
9780071445221
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For me, it was extremely difficult for the two years I spent learning Algebra 1. I'm in Geometry now and it's a little easier, but almost the same concept. Next year, I'll have to do Algebra 2, which I am NOT looking forward to.
Not if you learned the prerequisites. Essentially, did you learn what you should have in your lower level math classes? It sounds like you did. Don't sweat it. Pay attention, and study. Most importantly, dont be afraid to ask questions. If you don't understand something, ASK. You are in a place of learning, questions are expected, as it should be.
Keep up the good work.
Personally, I ask questions questions all the time, and enjoy it very much.
Algebra is not hard but most teachers and text books make it a nightmare... it should start as fun and puzzles and move to number patterns and interesting equations like motion, finance and measurement.. instead its taught as meaningless bunches of letters and many students' maths careers end with yr8 algebra and negative numbers. I'm a maths teacher.
Algebra is kind of hard when you are learning new concepts, but after you get the hang of it it's really not as hard as others say it is. No matter how hard it seems, study hard and try your best to understand it; you will need it later on. I am taking Geometry, and basically everything is based on what I learned last year in Algebra. That's the thing about math classes, they build on what you have learned in the past.
Hi sofia As a teacher I am surprised they ruin beautiful geometry (gemstones, navigation, art, tangram puzzles, design etc) by dragging in problems using algebra which will NEVER happen in higher level maths or real life. I'm thinking of like add the angles a + 2a = 90 degrees and more complex ones, its just an excuse to make more students fail by mixing skills, its not useful at all. Your advice to learn algebra is right, but its needed for "predicting the future" using equations in finance, risk, measurement (area/volume) and regulations on limits. Good luck in your studies.
Calculus is algebra but its nothing like as hard as people imagine from cartoons, its just that teachers teach it sooo badly. Differential Calculus is just GRADIENT (slope, tangent and a whole lot more same topic different names you have already done) Integral Calculus is just AREA. I believe year 11 and 12 maths up to calculus could be taught in 20 lessons. | 677.169 | 1 |
Overcoming MathThe new edition retains the author's pungent analysis of what makes math "hard" for otherwise successful people and how women, more than men, become victims of a gendered view of math. It has been substantially updated to incorporate new research on what we know and don't know about "sex differences" in brain organization and function, and it has been enlarged to include problems, puzzles, and strategies tried out in hundreds of math-anxiety workshops Tobias and her colleagues have sponsored. The author sees "math anxiety" as a political issue. So long as people believe themselves to be disabled in mathematics and do not rise up and confront the social and pedagogical origins of their disabilities, they will be denied "math mental health" - the willingness to learn the math you need when you need it. In an ever more technical society, that can make the difference between low and high self-esteem, failure and success. | 677.169 | 1 |
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Student Solutions Manual for Larson/Falvo's Elementary Linear Algebra, 7th:Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. | 677.169 | 1 |
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MAT-221 Mathematics for Elementary Teachers I4
credits
Prerequisites: MAT-105 or equivalent course with a minimum grade of C.
Topics include number systems, problem solving, sets, logic and properties of whole numbers and rational numbers. The emphasis is on mathematics taught in the elementary school classroom, using a variety of teaching techniques, methods, and hands-on materials including manipulatives and technology. | 677.169 | 1 |
Overview
This course aims to teach a suite of algorithms and concepts to a diverse set of participants interested in the general concept of fitting Data to Models.
Rather than starting with abstract Linear Algebra and staying on a highly mathematical path for most of the course, turning to some computation only towards the end, this course starts with mostly simple computational methods and introduces some more difficult mathematical concepts towards the end. This latter approach provides opportunities for much hands-on learning and participants leave with real practical knowledge of some of the basic algorithms. This method also, by design, fits in with our method of morning lectures and afternoon practice in the computer laboratory.
This is a very broad course and is intended only to cover the fundamentals of each technique we address. However, the gain is that we can cover many different approaches. Think of it this way: we cover the first chapter or two of a specialized 'book' on a given method. We get you through the fundamentals, which allow you to then get further through the book on your own. Another way of thinking of our approach is the analogy of a carpenter's tools. The goal is for participants to understand the utility of each tool, not to become specialists in any one method. In that sense, the course is introductory and general.
We tap into material from a very wide selection of literature in many disciplines involving computation, including but not limited to: statistics and applied mathematics, science, engineering, medicine and biomedicine, computer science, geosciences, system engineering, economics, insurance, finance, business, and aerospace engineering. More specific areas in which you might come across relevant books are: Regression, Non-linear Regression, Linear and Non-Linear Parameter Estimation, Inversion, System Identification, Econometrics, Biometrics, etc. The diversity of the participants and their fields provides many perspectives on our common interest in Data and Models.
Who Should Attend
Anyone who fits data to models. This course is truly broad-based and participants from vastly differing fields are envisioned and encouraged to attend. Some of these fields are engineering, business, natural sciences, geoscience, medicine, statistics, and economics.
Familiarity with computing and statistics is desirable. A fair background in linear algebra is highly recommended.
The course is a condensed version of a regular Fall MIT class with the same title, taught by Professor Morgan. The course has also been given at NASA, the University of the West Indies in Barbados, Sakarya University in Turkey, Stanford University, and Texas A&M University.
Program Outline
The format of each day is generally the same: mornings are devoted to lectures while participants spend the afternoons running pre-programmed software based on those lectures. During the afternoons, we often stop the class to have a discussion of progress and to give helpful tips. Students can work singly or in pairs at the computer. The computer exercises are usually done in one of the Athena cluster classrooms at MIT. However, we can make the executable programs available to run on your personal PC.
Individual lectures will address the following topics:
Philosophy of Data and Models
Statistics
Straight Line Data Analysis
Least Squares
Levenberg-Marquardt and Ridge Regression Algorithms
Damped Least Squares Comparison
Stochastic Inverse
Singular Value Decomposition
Random and Grid-Search Methods
Simulated Annealing and Genetic Algorithms
Neural Networks
Parameter Error Estimates
Large Inverse Problems
Experimental Design
Note that the order of the lectures can vary from that given above. A bound copy of all Power Point lecture notes is given to each student, to follow lectures and make notes.
Participants' Comments
Deputy Chief Scientist, Air Force Office of Scientific Research (AFOSR)
"The course efficiently provided a broad understanding of a wide variety of methods to a very varied and interesting group of students."
Associate Professor, University of the Pacific "Course was well designed. Lab work was very helpful. Application to real-world problems was well illustrated."
Electrical & Controls Engineer, BP America
I enjoyed the courses taken at MIT this summer. They combined a large amount of theory with lab work in an accelerated fashion. These courses have been the best post-bachelors courses I have taken thus far."
Postdoctoral Research Fellow, Brigham and Women's Hospital
"I found it to be a very stimulating and exciting environment. I felt that the instructors were very knowledgeable in the area and were willing to discuss issues related to applications beyond the classroom. Overall, I would attend courses at the MIT Professional Education - Short Programs in the future and would recommend the program to colleagues."
Instructors
Frank Dale Morgan obtained his BSc (Math/Physics, 1970) and his MSc (Theoretical Solid State Physics, 1972) from the University of the West Indies, Trinidad, where he was a Lecturer in Physics from 1970-1975. From 1975 to 1981, he completed a PhD in Geophysics at the Massachusetts Institute of Technology. He returned to the University of the West Indies, Trinidad, as a Research Fellow in the Seismic Research Unit. From 1983 to 1985 he was a Research Associate in the Geophysics Department at Stanford University. In 1985 he joined the faculty of the Geophysics Department at Texas A&M University. He is now a Professor of Geophysics at the Massachusetts Institute of Technology in the Department of Earth, Atmospheric, and Planetary Sciences and associated with the Earth Resources Laboratory. His current interests are in rock physics, geoelectromagnetism, applied seismology, inverse theory, environmental and engineering geophysics, electrochemistry, and electronic instrumentation. He teaches courses on the physics and chemistry of rocks, environmental and engineering geophysics, alternative energy, and inverse theory. He is the organizer and principal instructor for the course.
Darrell Coles obtained his BA in Pure Mathematics from the University of Rochester (1994) and his MSc in Geosystems (1998) and PhD in Geophysics (2008) from the Massachusetts Institute of Technology. He completed a joint postdoctoral fellowship with Total E&P and the University of Edinburgh in 2010. Since 2010, he has worked as a research scientist at Schlumberger. His current research interests are in optimal experimental design, inverse and optimization theory, reservoir geophysics, and uncertainty characterization and control.
Rama Rao is currently Senior Director and Head of Risk Analytics at PayPal. He leads a team of data analysts who monitor business performance and perform the analytics that go into creating PayPalís risk policies around the world—boundaries within which users can transact and experience PayPal. Rama has held various analytics roles within PayPal over the last five years, and has led several innovations in business analysis and has also helped build out the PayPalís risk analytics function in India. Prior to PayPal, Rama was at MIT for nine years where he led a research program, funded by an international consortium of oil majors and service companies, working on innovative uses of acoustic measurements to image and locate hydrocarbons. During this time, Rama taught a fall graduate course in data analytics along with Prof. Dale Morgan. Rama also spent a year at McKinsey where he worked on client initiatives aimed at creating new businesses that leverage existing assets and innovations. Rama continues to visit MIT every summer, to teach this course. Rama completed his undergraduate at the Indian Institute of Technology, Madras followed by dual Masters and a PhD at MIT.
Location
This course takes place on the MIT campus in Cambridge, Massachusetts. We can also offer this course for groups of employees at your location. Please contact the Short Programs office for further details. | 677.169 | 1 |
Covering the many aspects of geometry, this volume of the History of Mathematics series presents a compelling look at mathematical theories alongside historical occurrences. The engaging and informative text, complemented by photographs and illustrations, introduces students to the fascinating story of how geometry has developed. Biographical information on key figures, a look at different applications of geometry over time, and the groundbreaking discoveries related to geometry are comprehensively covered. | 677.169 | 1 |
The basics of computer algebra and the language of Mathematica are described. This title will lead toward an understanding of Mathematica that allows the reader to solve problems in physics, mathematics, and chemistry. Mathematica is the most widely used system for doing mathematical calculations by computer, including symbolic and numeric calculations... more...
Focusing on robust rank-based nonparametric methods, this book covers rank-based fitting and testing for models ranging from simple location models to general linear models for uncorrelated and correlated responses. Illustrated with real data examples using R, each chapter includes a short problem set with data sets. The corresponding example codes... more... more education, psychology, and sensory science. Written... more...
This handbook shows how to use SAS to create many different types of useful statistical graphics for exploring data and diagnosing fitted models. The book focuses on the relatively new SAS ODS graphics, including graphs that are produced routinely via ODS and more tailored graphics. Each chapter deals graphically with several sets of data from a wide... more...
This book brings together contributed papers presenting new results covering different areas of applied mathematics and scientific computing. Firstly, four invited lectures give state-of-the-art presentations in the fields of numerical linear algebra, shape preserving approximation and singular perturbation theory. Then an overview of numerical solutions... more... | 677.169 | 1 |
Counting to Calculating, part of the Mathematics for the Majority series produced by The Schools Council Project in Secondary School Mathematics, is aimed at expanding teachers' knowledge about the use of number in calculations in order to pass on this understanding to higher secondary students within their lessons. This…
Number Appreciation, part of the Mathematics for the Majority series produced by The Schools Council Project in Secondary School Mathematics, is aimed at expanding teachers' knowledge about the number system in order to pass on this understanding to higher secondary students within their lessons. This book compliments From…
Mathematics From Outdoors, part of the Mathematics for the Majority series produced by The Schools Council Project in Secondary School Mathematics, is aimed at expanding teachers' knowledge and is designed to help teachers to develop classroom activities that will interest students and enable them to link the mathematics they…
Machines, Mechanisms and Mathematics, part of the Mathematics for the Majority series produced by The Schools Council Project in Secondary School Mathematics, is aimed at expanding teachers' knowledge, and is written in the belief that much of mathematics has been developed to solve practical problems.
Many practical applications…
Luck and Judgement, part of the Mathematics for the Majority series produced by The Schools Council Project in Secondary School Mathematics, is aimed at expanding teachers' knowledge, concentrating upon a practical approach to the teaching of probability and statistics.
The book has two parts, the first concentrating upon…
Crossing Subject Boundaries, part of the Mathematics for the Majority series produced by The Schools Council Project in Secondary School Mathematics, is a book aimed at teachers, encouraging collaboration across different subject areas.
Each chapter focuses upon a different area of the curriculum and describes aspects of mathematics…
This book first published in 1977 is about graphs, their drawing, their interpretation, their development and their use. It discusses the teaching of graphs from their early introduction and as far as the beginnings of integral and differential calculus. The book also places the teaching of graphs in an historical context as it reviews Schools Council publication addresses assignment cards and how they can play an important part in mathematics teaching. The book discusses methods of preparing them and gives numerous examples.
Topics as diverse as the Binary system, punched card matrices, vectors and topology feature as do geometrical and statistical assignments. is one of the Mathematics for the Majority project's background guides. It brings together, from a variety of branches of mathematics, topics in which an element of pattern is strongly emphasised. In particular, the chapters cover:
1. Pattern's pervasiveness
2. Some patterns in numbers
3.…
This unit from the Continuing Mathematics Project is designed to enable students to cope confidently with expressions of the type A/B= C/D, where A, B, C and D, may be integers or algebraic products like mv2 or functions like log x, or sin y.
So equipped, students will be able to solve simple equations, change the subject of a…
This unit from the Continuing Mathematics Project goes into detail on how logarithms can be used to determine the laws which connect two variables on which experimental data has been collected. The unit follows naturally from the unit entitled The Theory of Logarithms.
The objectives of the unit are that students:
(i) understand…
Transformation of Formulae from the Continuing Mathematics Project builds on the work covered in the unit entitled Working with Ratios.
The objectives of this unit are to enable students to acquire the skills necessary to transform formulae which involve algebraical fractions, brackets, and roots, as well as formulae in which…
This unit from the Continuing Mathematics Project is concerned with the calculation of the sides and angles of triangles and how this is used by the surveyor, the navigator, and the cartographer. The development of the television, the light and the road have all relied on trigonometry.
The objectives of the unit are that students…
This is the second part of the unit on The Theory of Logarithms from the Continuing Mathematics Project. It assumes that the user has completed the first part of the unit.
The objectives of the unit are to enable students to:
(i) acquire the concept of a logarithm as an extension of the concepts of a 'power' and of…
These two units from the Continuing Mathematics Project assumes that the word 'logarithm' will be familiar to students using it, and that they will have used tables of logarithms to reduce the labour of working out expressions by arithmetic methods.
The units assume that students are interested in knowing why logarithms…
This resource from the Continuing Mathematics Project has three units covering probability.
Introducing Probability is the first unit and its objectives are that students will learn that a probability can be from intuitive considerations or actual experimental results; the meaning of 'outcomes', 'sample space',…
This unit from the Continuing Mathematics Project assumes that students have met and used directed numbers, but that their use has become rusty. The unit briefly justifies the rules by which the four operations (+, -, x and ÷) can be accurately carried out. In this sense the unit could be said to form an introduction to the…
For students to benefit from this Mathematics in Geography 4 unit from the Continuing Mathematics Project they should be familiar with simple ratios and square roots, and with algebraic symbolism and quadratic equations. A fair amount of arithmetic is involved in the unit.
The objectives of the unit are;
(i) to introduce students…
This unit from the Continuing Mathematics Project is about linear programming - a procedure which is used widely in industry to solve management problems. The work here is an introduction to the subject.
There are no really new mathematical techniques in the unit. It is rather an amalgamation of things students have probably learnt…
This unit from the Continuing Mathematics Project has been planned to help students learn how to handle inequalities, and how to represent them graphically. Students should be familiar with manipulating positive and negative numbers, representing equations of the form y + 3x = 6 as a graph and finding the solution of equations like unit from the Continuing Mathematics Project on flowcharts and Algorithms employs, three basic conventions:
(i) the use of a flowchart and the appropriate symbols
(ii) the use of computer statements, such as 'c = c + I1
(iii) the use of the inequality signs >, <, ≤ and ≥
Three very short programmes at the…
Descriptive Statistics is the name the continuing Mathematic Project has given to a sequence of four units which deal with distributions, histograms, bar charts, frequency tables and measures of central tendency and dispersion.
The first unit, Presenting Statistics, aims to teach some basic statistical techniques that are useful…The first half of the unit is devoted to exposition and illustration of…
This unit from the Continuing Mathematics Project is about the relationship between two quantities (correlation). If the two quantities are height of father and height of son, then we often want to know the extent to which 'tall fathers have tall sons'. Two quantities may be correlated quite strongly while another two quantities……
This Mathematics Curriculum book, first published in 1977, intended to act as an aid and catalyst in co-operation between teachers of mathematics and teachers of other subjects which use mathematics. It looks at areas of applied mathematics that demonstrate its usefulness and are of genuine interest to other subject areas. A knowledge… | 677.169 | 1 |
Objectives: To explore trigonometric functions
including identities, definitions, radian measure, graphs, solving equations,
vectors, law of sines, law of cosines, complex
numbers, and polar coordinates. A graphing calculator is required; a TI-(83-86)
or equivalent is recommended. The class will be taught using these calculators
and you will be allowed to use yours on indicated test problems.
Policies and Procedures:
1.Attendance is expected. Miss Stoker's
rules for class attendance and tardies will be
followed and I endorse it.
2.Complete each homework (HW)
assignment as assigned before the next class meeting – this will facilitate
understanding of the following lecture. As this is a college class, it will
move quickly and two hours of HW for each class is not excessive. Also, some
independence of thought is necessary since everything that will show up on your
HW cannot be covered during class time. Therefore, the best way to do well on
tests is to do your HW as independently as possible and to spend the necessary
time trying to understand everything on your own – especially HW problems that
give you trouble. Getting immediate help on a hard problem doesn't prepare you
for tests. Miss Stoker will decide which days HW is to be handed in. Your HW
should be neat and show complete work wherever it is necessary to solve a
problem. Late HW will notbe accepted unless you have a legitimate
excuse (the same as for tests – see #3). Miss Stoker will decide whether a late
assignment can be turned in based on the reason for it being late.
3.Should you have
to miss class on the day of a test, you must contact Miss Stoker as soon as
possible to schedule a makeup test. If you wait longer than one day to contact
her the score on the test you miss will simply be a zero regardless of excuse.
Legitimate excuses are such things as school-excused absences, having to be
gone for a family wedding or funeral, significant illness and so on. Sleeping
through an alarm or missing a test because you didn't know when it was are not
legitimate and will result in a zero on the test. Miss Stoker will make all
decisions on whether a makeup is warranted based on policy in this syllabus.
Take tests seriously since they make up the bulk of your grade.
4.Scholastic dishonesty will not be
tolerated and will be fully prosecuted. HW plagiarism
(copying from a solutions manual or someone else's HW) will result in a zero on
any assignment; if it is repeated, you will get a zero on the entire HW score
of 50 points. Passing any test information to another student that
hasn't yet taken it is prohibited and dishonest and will result in a failing
grade in the course.
5.GradingThe
total will be 600 points, including a total of 50 points from HW, 400 from the
one-hour tests and 150 from the final exam. The grading scale will be the
following: Please note that I cannot raise a grade because of need, so it is up
to you to get the grade you want. | 677.169 | 1 |
books.google.co.jp to the theory of nonlinear elliptic equations | 677.169 | 1 |
This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.
Finite such as "Your Turn" exercises and "Apply It" vignettes that encourage active participation
Anton, Bivens & Davis latest issue of Calculus Early Transcendentals Single Variable continues to build upon previous editions to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds.
This text helps students improve their understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. Over 1,200 problems, with hints and complete solutions. Topics include sequences, functions of a single variable, limit of a function, differential calculus for functions of a single variable, the differential, indefinite and definite integrals, more. 1963 edition. | 677.169 | 1 |
Geometry Jurgensen Teachers Edition PDF
This courses uses the 2011 edition of the Jurgensen, Brown, and Jurgensen textbook, ... and Jurgensen, Geometry. Houghton Mifflin, 2011. Teachers use other texts for supplementary ideas, such as Discovering Geometry by Michael Serra, and also current mathematical
This course use the 2000 edition of the Jurgensen, Brown, and Jurgensen textbook, ... and Jurgensen, Geometry. Houghton Mifflin, 2000. Teachers use other texts for supplementary ideas, such as Discovering Geometry by Michael Serra, and also current mathematical
The teachers worked alone or in pairs to develop a plan for a section of the course. Jim Beamer, University of Saskatchewan, and Lyle Markowski, ... Examples from Geometry - Jurgensen 1985 edition could include: PAGE SUITABLE QUESTIONS 13 classroom exercises 1-38
Ray Jurgensen, Richard Brown, and John Jurgensen Students and Grade Levels ... Geometry, Pupil's Edition ... provide service to teachers. This service is available from 8 a.m. to 5 p.m. CST, Monday through Friday. Page 4
... they are the correct edition and 2) ... GEOMETRY by Jurgensen, Brown & Jurgensen Houghton-Mifflin College 9780395977279 $109.00 Follett ... HISTORY ALIVE: ANCIENT WORLD by Teachers Curriculum Inst Student Bundle, Item #TB-9015-6 - Available only through Publisher at | 677.169 | 1 |
A collection of illustrated concepts including problems for students to work out, and standalone word problems. Includes automated feedback. Pre- and post-tests, answer sheets, additional help, tools, and a bulletin board are also included | 677.169 | 1 |
77 minute basic algebra lesson will introduce you to five types of word problems that are applications of linear equations. This lesson will show you first how to translate the words into algebra and then how to solve:
- number problems
- age problems (like "Kevin is 3 times as old as his nephew, Doug. Two years ago, Kevin was 5 times as old as Doug was 4 years ago. Find their present ages.")
- coin problems
- mixture problems
- distance rate and time problems
This lesson contains explanations of the concepts and 20 example questions with step by step solutions plus 5 | 677.169 | 1 |
Geoffrey C. Berresford, Long Island University
Andrew M. Rockett, Long Island University
This
new program will help you understand the best uses for the technology
supplements that accompany your textbook. Click the icons above or
the links to the left for more information or to access any of the
web-based products.
Introduction to ExcelBasics of the TI-83 Basics of the TI-83 is a walkthrough of specific graphing calculator functions. You will learn how to: plot a function, change dimensions of the viewing rectangle, determine intercepts graphically and numerically, model data using regression, and compute factorials and permutations.
Student Solutions Manual
This will link you to a sample chapter (Chapter 1) of the Student Solutions Manual, which shows the worked out, step-by-step solutions to all odd exercises, and all Chapter Review exercises, in your text. If you'd like to purchase the Student Solutions Manual go to math.college.hmco.com/students and link to our on-line Bookstore.
Prerequisite Algebra
Review
The Prerequisite Algebra Review provides students with a quick review of algebra skills whenever they need it. Students can select a topic from an
extensive list and walk through the short lesson and examples provided.
Projects and Essays The Projects and Essays listed below accompany each section of your text. Your instructor might assign them as a group project or as an individual project, and in either case they will allow you to display your knowledge of the material in a way different from quizzes or tests. If you are using Brief Applied Calculus, please note that sections 6.5 and 6.6 in your book are equivalent to sections 9.1 and 9.2 in the Applied Calculus Table of Contents.
Graphing Calculator Help Visit the Texas Instrument link below to view the combination of equipment that will work with your calculator.
Excel Spreadsheet Explorations Chapters 1-7 of your text each contain an Excel Spreadsheet Exploration. This link will access each of the data sets, organized by chapter, that you will need to complete the Exploration.
Graphing Calculator Programs The following Texas Instruments graphing calculator programs are available for the TI-82, TI-83, TI-85, TI-86, TI-89 and TI-92 for use on either Mac or PC computers. The programs correspond to those referenced in your text. | 677.169 | 1 |
More About
This Textbook
Overview
An exciting edition of this practical math methods book that provides future teachers with practical procedures for increasing student success in math. Emphasizing specific, classroom-tested strategies, these authors provide techniques for teaching major math and needed prerequisite skills, as well as extensive background in diagnosing and correcting error patterns. In addition, they offer practical guidelines for curriculum evaluation and modification, recommendations for practice and review drills, and specific information on progress-monitor | 677.169 | 1 |
Intermediate level mathematics for GCSE maths, High School math and many international secondary school courses.
Sections are broadly divided under UK & USA headings:
Number
Pre-Algebra
Algebra
Algebra-1
Shape & Space
Trigonometry & Geometry
Information
Statistics
Yes you can improve your grades! But only by hard work. There are no quick fixes. Read the notes, watch the videos and play with the interactives. It is also important to get lots and lots of practice. So use the worksheets and exam papers. These will help your understanding and boost confidence.
WORKSHEETS e-book volume 1 to download FREE
worksheets & answers on every topic
four sections to collect
GCSE Maths Tutor's topic revision notes released as four e-books to download FREE. | 677.169 | 1 |
To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how …Based on the author's junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for …. …
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to theBridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic. The author builds logic and mathematics | 677.169 | 1 |
books.google.co.jp - A.... mathematical introduction to logic
A mathematical introduction to logic
A. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.* Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students
この書籍内から
Review: A Mathematical Introduction to Logic
I love terse books, but even for me this book is too terse. It could really benefit from additional samples and explanations.レビュー全文を読む
Review: A Mathematical Introduction to Logic
ユーザー レビュー - DJ - Goodreads
The book accompanying a course taught by Len Adleman, co-inventor of RSA encryption, father of DNA computing, and a stellar lecturer. Poor textbook is doomed to be the forgotten stepchild of this course.レビュー全文を読む | 677.169 | 1 |
Introduction to Scientific, Symbolic, and Graphical Computation
9781568810515
ISBN:
1568810512
Publisher: A K Peters, Limited
Summary: This down-to-earth introduction to computation makes use of the broad array of techniques available in the modern computing environment. A self-contained guide for engineers and other users of computational methods, it has been successfully adopted as a text in teaching the next generation of mathematicians and computer graphics majors | 677.169 | 1 |
Calculus has been so successful reducing complicated problems to simple rules and procedures. Therein lies the danger in teaching calculus: it is possible to teach the subject as nothing but the rules and procedures -- thereby losing sight of both the mathematics and of its practical value. -- "Calculus" by Hughes-Hallett et. al.
In the late 1980's United States, rose a movement called "Calculus Reform". It was intended to take the place of traditional instruction which put too much emphasis on manual arithmetic. In this talk the spirit of reform is introduced with many examples. We mainly discuss on the elementary calculus (HS level calculus, MA 203 and 204 at UOG). The talk would be also beneficial to those studying advanced topics like MA 205, 302, 421 and 422.
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The Challenges in Mathematics Colloquium Lecture Series is organized by the Division of Mathematical Sciences of the Colleges of Natural and Applied Sciences of the University of Guam. It is usually held at 3:30 – 4:20 p.m. on the 4th Friday of every month during the semester. Our location is at the Division of Mathematical Sciences in Science Building Room 120 next to the Health-Science Building. Our intention is to introduce a wider audience of those who are interested in mathematical challenges into state-of-the-art mathematical theories, puzzles and open problems. We invite students, colleagues working in any area of science and everybody who wants to learn more about mathematics in an accessible and popular setting. | 677.169 | 1 |
Math in the News: AP Calculus
Double-click
any word to see the explanation.
AP Calculus, also known as Advanced Placement Calculus or AP Calc, is used to indicate one of two distinct Advanced Placement courses and examinations offered by the College Board, AP Calculus AB and AP Calculus BC.
Calculus is a branch of mathematics that includes the study of limits, derivatives, integrals, and infinite series, and constitutes a major part of modern university education. Historically, it was sometimes referred to as "the calculus of infinitesimals", but that usage is seldom seen today. Calculus has widespread applications in science and engineering and is used to solve problems for which algebra alone is insufficient. Calculus builds on algebra, trigonometry, and analytic geometry and includes two major branches, differential calculus and integral calculus, that are related by the fundamental theorem of calculus. In more advanced mathematics,
calculus is usually called analysis and is defined as the study of functions. | 677.169 | 1 |
More About
This Textbook
Overview
This book, based on a first-year graduate course the author taught at the University of Wisconsin, contains more than enough material for a two-semester graduate-level abstract algebra course, including groups, rings and modules, fields and Galois theory, an introduction to algebraic number theory, and the rudiments of algebraic geometry. In addition, there are some more specialized topics not usually covered in such a course. These include transfer and character theory of finite groups, modules over artinian rings, modules over Dedekind domains, and transcendental field extensions. This book could be used for self study as well as for a course text, and so full details of almost all proofs are included, with nothing being relegated to the chapter-end problems. There are, however, hundreds of problems, many being far from trivial. The book attempts to capture some of the informality of the classroom, as well as the excitement the author felt when taking the corresponding course as a student.
Editorial Reviews
Booknews
The author encourages students to develop an appreciation of how basic algebra is put together. The text is in two sections: noncommutative algebra, including homomorphisms, Sylow theorems, and rings; and commutative algebra, with polynomial rings, Galois theory, finite fields, Noetherian rings, and Dedekind domains. Discussion of such topic as the factorization algorithm of polynomials over finite fields gives students insight into the types of algorithms that underlie computer algebra software. Problems follow each chapter | 677.169 | 1 |
What is Mathematica?
Mathematica is the world's most powerful global computing environment. Ideal for use in engineering, mathematics, finance, physics, chemistry, biology, and a wide range of other fields, it makes possible a new level of automation in algorithmic computation, interactive manipulation, and dynamic presentation--as well as a whole new way of interacting with the world of data.
Getting Mathematica...
Mathematica is currently installed in the following locations:
Computer labs: Miller 20, Blaney 8, the Eisenhower Lab
Mathematica can also be installed on:
Faculty/staff school-owned machines: Installers are available at your IT helpdesk.
Students' personally-owned machines: Students can buy discounted licenses through Wolfram's Web store, but if you're teaching with Mathematica or lots of students will be purchasing licenses, please contact Andy Dorsett for better discounts.
Are you interested in putting Mathematica elsewhere? Please let IT or Andy Dorsett know.
What are the best steps to start using Mathematica?
If you are brand-new to Mathematica, below are some suggestions on the best ways to get started. | 677.169 | 1 |
Math Center Resources
The greatest of resources the Math Center has is its competent and friendly personnel. In addition, it has many other resources to help its customers. These resources include K-8 mathematics software, reference books and magazines, manipulatives, construction tools, geometrical models and instructional videotapes, there are currently four computers available for student use. Students can also use our Die Cutting Machine to make their own economical copies of the manipulatives that are used in class.
The Math Center also has its own video recording and playback equipment, so that students can view mathematics videotapes in order to review for their classes. We also hold Problem / Review Sessions typically on a weekly basis for Math 3032 so that students can get extra help on their homework or review concepts for upcoming tests/finals. In co-ordination with the Department of Mathematical Sciences, the Career and Counseling Center holds student workshops in the Math Center aimed at helping students prepare for exams and overcome math anxiety. | 677.169 | 1 |
books.google.com - The book is a thorough treatment of the mathematical theory and practical applications of compound interest, or mathematics of finance.... theory of interest | 677.169 | 1 |
Summary: The authors help students ''see the math'' through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to mathematical understanding and, ultimately, success in class.
This is a very good copy with slight wear. The dust jacket is included if the book originally was published with one and could have very slight tears and rubbing.
$2.46 +$3.99 s/h
VeryGood
Wiz Kids Books Irmo, SC
Tight & Clean. Light edge wear to cover
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New
Bookbyte-OR Salem, OR
New Condition. SKU:9780321531926-1-0
$2.8998Bookmans AZ Tucson, AZ
2008 Hardcover Good Satisfaction 100% guaranteed.
$6.57 +$3.99 s/h
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CampusBookRentals Ogden, UT
2008 Other 4th ed. Fair. Bittinger Graphs & Models39 +$3.99 s/h
Good
DOLLHOUSE BOOKS CALUMET CITY, IL
Good INCLUDES GRAPHING CALCULATOR MANUAL. BOK IS IN GOOD CONDITION BUT HAS VERY SLIGHT RAIN DAMAGE ON THE TOP EDGE OF SOME PAGES. DOES NOT INTERFERE WITH THE READING OF THE PAGES. BOOK IS CLEAN INSI...show moreDE. COVER MAY HAVE SLIGHT WEAR ON CORNERS. WILL SHIP BEST AVAILABLE | 677.169 | 1 |
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
New Maths Frameworking Y9 Pupil Book 3 APP chart
Levels Using and applying mathematics Book references
Level 8 develop and follow alternative methods and
approaches
reflect on lines of enquiry when exploring
mathematical tasks
select and combine known facts and problem
solving strategies to solve problems of increasing
complexity
convey mathematical meaning through precise
and consistent use of symbols
examine generalisations or solutions reached in an
activity, commenting constructively on the
reasoning and logic or the process employed, or
the results obtained
distinguish between practical demonstration and
proof; know underlying assumptions, recognising
their importance and limitations, and the effect of
varying them
Level 7 solve increasingly demanding problems and
evaluate solutions; explore connections in
mathematics across a range of contexts: number,
algebra, shape, space and measures, and
handling data; refine or extend the mathematics
used to generate fuller solutions
give reasons for choice of presentation, explaining
selected features and showing insight into the
problems structure
justify generalisations, arguments or solutions 14B, 14D
appreciate the difference between mathematical 15B
explanation and experimental evidence
Level 6 solve problems and carry through substantial tasks Pages 208-9
by breaking them into smaller, more manageable
tasks, using a range of efficient techniques,
methods and resources, including ICT; give
solutions to an appropriate degree of accuracy
interpret, discuss and synthesise information
presented in a variety of mathematical forms
present a concise, reasoned argument, using 14B, 14D
symbols, diagrams, graphs and related
explanatory texts
use logical argument to establish the truth of a
statement
Level 5 identify and obtain necessary information to carry Pages 14-15, pages 80-81,
through a task and solve mathematical problems pages 144-5, pages 156-7,
pages 192-3
check results, considering whether these are
reasonable
solve word problems and investigations from a Pages 40-41, pages 106-7
range of contexts
show understanding of situations by describing
them mathematically using symbols, words and
diagrams
draw simple conclusions of their own and give an
explanation of their reasoning
Level 4 develop own strategies for solving problems
use their own strategies within mathematics and in
applying mathematics to practical contexts
present information and results in a clear and
* Part of the criteria are covered 1
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
organised way
search for a solution by trying out ideas of their
own
Level 3 select the mathematics they use in a wider range
of classroom activities
try different approaches and find ways of
overcoming difficulties that arise when they are
solving problems
begin to organise their work and check results
use and interpret mathematical symbols and
diagrams
understand a general statement by finding
particular examples that match it
review their work and reasoning
Level 2 select the mathematics they use in some
classroom activities
discuss their work using mathematical language
begin to represent their work using symbols and
simple diagrams
predict what comes next in a simple number,
shape or spatial pattern or sequence and give
reasons for their opinions
explain why an answer is correct
* Part of the criteria are covered 2
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
Levels Numbers and the number system Book references
Level 8 understand the equivalence between recurring 7F
decimals and fractions
Level 7 understand and use proportionality 2D
Level 6 use the equivalence of fractions, decimals and
percentages to compare proportions
Level 5 use understanding of place value to multiply and
divide whole numbers and decimals by 10, 100
and 1000 and explain the effect
round decimals to the nearest decimal place and
order negative numbers in context
recognise and use number patterns and
relationships
use equivalence between fractions and order
fractions and decimals
reduce a fraction to its simplest form by cancelling
common factors
understand simple ratio
Level 4 recognise and describe number patterns
recognise and describe number relationships
including multiple, factor and square
use place value to multiply and divide whole
numbers by 10 or 100
recognise approximate proportions of a whole and
use simple fractions and percentages to describe
these
order decimals to three decimal places
begin to understand simple ratio
Level 3 understand place value in numbers to 1000
use place value to make approximations
recognise negative numbers in contexts such as
temperature
use simple fractions that are several parts of a
whole and recognise when two simple fractions are
equivalent
begin to use decimal notation in contexts such as
money
Level 2 count sets of objects reliably
begin to understand the place value of each digit;
use this to order numbers up to 100
begin to use halves and quarters and relate the
concept of half of a small quantity to the concept of
half of a shape
* Part of the criteria are covered 3
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
Levels Calculating Book references
Level 8 use fractions or percentages to solve problems 2B-C
involving repeated proportional changes or the
calculation of the original quantity given the result
of a proportional change
solve problems involving calculating with powers, 7A-B*, 7G*
roots and numbers expressed in standard form,
checking for correct order of magnitude and using
a calculator as appropriate
Level 7 calculate the result of any proportional change 2B, 2D
using multiplicative methods
understand the effects of multiplying and dividing 2F-G
by numbers between 0 and 1
add, subtract, multiply and divide fractions 2A
make and justify estimates and approximations of 2H
calculations; estimate calculations by rounding
numbers to one significant figure and multiplying
and dividing mentally
use a calculator efficiently and appropriately to 7G
perform complex calculations with numbers of any
size, knowing not to round during intermediate
steps of a calculation
Level 6 calculate percentages and find the outcome of a
given percentage increase or decrease
divide a quantity into two or more parts in a given
ratio and solve problems involving ratio and direct
proportion
use proportional reasoning to solve a problem,
choosing the correct numbers to take as 100%, or
as a whole
add and subtract fractions by writing them with a
common denominator, calculate fractions of
quantities (fraction answers), multiply and divide
an integer by a fraction
Level 5 use known facts, place value, knowledge of
operations and brackets to calculate including
using all four operations with decimals to two
places
use a calculator where appropriate to calculate
fractions/percentages of quantities/measurements
understand and use an appropriate non-calculator
method for solving problems that involve
multiplying and dividing any three digit number by
any two digit number
solve simple problems involving ordering, adding,
subtracting negative numbers in context
solve simple problems involving ratio and direct
proportion
apply inverse operations and approximate to check
answers to problems are of the correct magnitude
Level 4 use a range of mental methods of computation
with all operations
recall multiplication facts up to 10 × 10 and quickly
derive corresponding division facts
use efficient written methods of addition and
subtraction and of short multiplication and division
multiply a simple decimal by a single digit
* Part of the criteria are covered 4
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
solve problems with or without a calculator
check the reasonableness of results with reference
to the context or size of numbers
Level 3 derive associated division facts from known
multiplication facts
add and subtract two digit numbers mentally
add and subtract three digit numbers using written
method
multiply and divide two digit numbers by 2, 3, 4 or
5 as well as 10 with whole number answers and
remainders
use mental recall of addition and subtraction facts
to 20 in solving problems involving larger numbers
solve whole number problems including those
involving multiplication or division that may give
rise to remainders
Level 2 use the knowledge that subtraction is the inverse
of addition and understand halving as a way of
'undoing' doubling and vice versa
use mental recall of addition and subtraction facts
to 10
use mental calculation strategies to solve number
problems including those involving money and
measures
record their work in writing
choose the appropriate operation when solving
addition and subtraction problems
* Part of the criteria are covered 5
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
Levels Algebra Book references
Level 8 factorise e.g. quadratic expressions including the 11D
difference of two squares,
2
x – 9 = (x + 3) (x – 3)
manipulate algebraic formulae, equations and 11A-C
expressions, finding common factors and
multiplying two linear expressions
derive and use more complex formulae and 11E*
change the subject of a formula
evaluate algebraic formulae, substituting fractions,
decimals and negative numbers
solve inequalities in two variables and find the 3E extension*
solution set
sketch, interpret and identify graphs of linear,
quadratic, cubic and reciprocal functions, and
graphs that model real situations
understand the effect on a graph of addition of (or
multiplication by) a constant
Level 7 square a linear expression, and expand and 11C
simplify the product of two linear expressions of
the form (x ± n) and simplify the corresponding
quadratic expression
use algebraic and graphical methods to solve 3B-C, 3G
simultaneous linear equations in two variables
solve inequalities in one variable and represent the 3E
solution set on a number line
use formulae from mathematics and other 11E
subjects; substitute numbers into expressions and
formulae; derive a formula and, in simple cases,
change its subject
find the next term and nth term of quadratic 1B
sequences and functions and explore their
properties
plot graphs of simple quadratic and cubic 8C-D
2 2
functions, e.g. y = x , y = 3x + 4,
3
y=x
Level 6 use systematic trial and improvement methods and
ICT tools to find approximate solutions to
3
equations such as x + x = 20
construct and solve linear equations with integer 3A, 3D
coefficients, using an appropriate method
generate terms of a sequence using term-to-term 1A*
and position-to-term definitions of the sequence,
on paper and using ICT; write an expression to
describe the nth term of an arithmetic sequence
plot the graphs of linear functions, where y is given
explicitly in terms of x; recognise that equations of
the form y = mx + c correspond to straight-line
graphs
construct functions arising from real-life problems 1D*, 3F
and plot their corresponding graphs; interpret
graphs arising from real situations
Level 5 construct, express in symbolic form, and use
simple formulae involving one or two operations
use and interpret coordinates in all four quadrants
Level 4 begin to use simple formulae expressed in words
use and interpret coordinates in the first quadrant
* Part of the criteria are covered 6
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
Level 3 recognise a wider range of sequences
begin to understand the role of '=' (the 'equals'
sign)
Level 2 recognise sequences of numbers, including odd
and even numbers
* Part of the criteria are covered 7
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
Levels Shape, space and measure Book references
Level 8 understand and use congruence and mathematical 2E*, 4D*, 6A
similarity
understand and use trigonometrical relationships in 10B-D
right-angled triangles, and use these to solve
problems, including those involving bearings
understand the difference between formulae for
perimeter, area and volume in simple contexts by
considering dimensions
Level 7 understand and apply Pythagoras' theorem when 4A-B
solving problems in 2-D
calculate lengths, areas and volumes in plane 6D*, pages 124-5
shapes and right prisms
enlarge 2-D shapes, given a centre of enlargement 10A
and a fractional scale factor, on paper and using
ICT; recognise the similarity of the resulting shapes
find the locus of a point that moves according to a 4C
given rule, both by reasoning and using ICT
recognise that measurements given to the nearest
whole unit may be inaccurate by up to one half of
the unit in either direction
understand and use measures of speed (and other 6E
compound measures such as density or pressure)
to solve problems
Level 6 classify quadrilaterals by their geometric properties
solve geometrical problems using properties of
angles, of parallel and intersecting lines, and of
triangles and other polygons
identify alternate and corresponding angles;
understand a proof that the sum of the angles of a
triangle is 180° and of a quadrilateral is 360°
devise instructions for a computer to generate and
transform shapes and paths
visualise and use 2-D representations of 3-D
objects
enlarge 2-D shapes, given a centre of enlargement
and a positive whole-number scale factor
know that translations, rotations and reflections
preserve length and angle and map objects onto
congruent images
use straight edge and compasses to do standard 4C
constructions
deduce and use formulae for the area of a triangle
and parallelogram, and the volume of a cuboid;
calculate volumes and surface areas of cuboids
know and use the formulae for the circumference
and area of a circle
Level 5 use a wider range of properties of 2-D and 3-D
shapes and identify all the symmetries of 2-D
shapes
use language associated with angle and know and
use the angle sum of a triangle and that of angles
at a point
reason about position and movement and
transform shapes
measure and draw angles to the nearest degree,
when constructing models and drawing or using
* Part of the criteria are covered 8
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
shapes
read and interpret scales on a range of measuring
instruments, explaining what each labelled division
represents
solve problems involving the conversion of units
and make sensible estimates of a range of
measures in relation to everyday situations
understand and use the formula for the area of a
rectangle and distinguish area from perimeter
Level 4 use the properties of 2-D and 3-D shapes
make 3-D models by linking given faces or edges
and draw common 2-D shapes in different
orientations on grids
reflect simple shapes in a mirror line, translate
shapes horizontally or vertically and begin to rotate
a simple shape or object about its centre or a
vertex
choose and use appropriate units and instruments
interpret, with appropriate accuracy, numbers on a
range of measuring instruments
find perimeters of simple shapes and find areas by
counting squares
Level 3 classify 3-D and 2-D shapes in various ways using
mathematical properties such as reflective
symmetry for 2-D shapes
begin to recognise nets of familiar 3-D shapes, e.g.
cube, cuboid, triangular prism, square-based
pyramid
recognise shapes in different orientations and
reflect shapes, presented on a grid, in a vertical or
horizontal mirror line
describe position and movement
use a wider range of measures including non-
standard units and standard metric units of length,
capacity and mass in a range of contexts
use standard units of time
Level 2 use mathematical names for common 3-D and 2-D
shapes
describe their properties, including numbers of
sides and corners
describe the position of objects
distinguish between straight and turning
movements, recognise right angles in turns and
understand angle as a measurement of turn
begin to use a wider range of measures including
to use everyday non-standard and standard units
to measure length and mass
begin to understand that numbers can be used not
only to count discrete objects but also to describe
continuous measures
* Part of the criteria are covered 9
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
Levels Handling data Book references
Level 8 estimate and find the median, quartiles and 5E
interquartile range for large data sets, including
using a cumulative frequency diagram
compare two or more distributions and make
inferences, using the shape of the distributions and
measures of average and spread including median
and quartiles
know when to add or multiply two probabilities 9C
use tree diagrams to calculate probabilities of 9C
combinations of independent events
Level 7 suggest a problem to explore using statistical 13B
methods, frame questions and raise conjectures;
identify possible sources of bias and plan how to
minimise it
select, construct and modify, on paper and using 5B*, 13B
ICT suitable graphical representation to progress
an enquiry including frequency polygons and lines
of best fit on scatter graphs
estimate the mean, median and range of a set of 5F*
grouped data and determine the modal class,
selecting the statistic most appropriate to the line of
enquiry
compare two or more distributions and make
inferences, using the shape of the distributions and
measures of average and range
understand relative frequency as an estimate of 9D, 15B
probability and use this to compare outcomes of an
experiment
examine critically the results of a statistical enquiry, 13B
and justify the choice of statistical representation in
written presentation
Level 6 design a survey or experiment to capture the 5G
necessary data from one or more sources; design,
trial and, if necessary, refine data collection sheets;
construct tables for large discrete and continuous
sets of raw data, choosing suitable class intervals;
design and use two-way tables
select, construct and modify, on paper and using
ICT and identify which are most useful in the
context of the problem:
pie charts for categorical data
bar charts and frequency diagrams for discrete
and continuous data
simple time graphs for time series
scatter graphs
find and record all possible mutually exclusive
outcomes for single events and two successive
events in a systematic way
know that the sum of probabilities of all mutually 9B
exclusive outcomes is 1 and use this when solving
problems
communicate interpretations and results of a Pages 172-3
statistical survey using selected tables, graphs and
diagrams in support
Level 5 ask questions, plan how to answer them and collect
the data required
* Part of the criteria are covered 10
Assessment criteria: New Maths Frameworking Year 9 Pupil Book 3
in probability, select methods based on equally
likely outcomes and experimental evidence, as
appropriate
understand and use the probability scale from 0 to
1
understand and use the mean of discrete data and
compare two simple distributions, using the range
and one of mode, median or mean
understand that different outcomes may result from
repeating an experiment
interpret graphs and diagrams, including pie charts, 5C-D
and draw conclusions
create and interpret line graphs where the
intermediate values have meaning
Level 4 collect and record discrete data
group data, where appropriate, in equal class
intervals
continue to use Venn and Carroll diagrams to
record their sorting and classifying of information
construct and interpret frequency diagrams and
simple line graphs
understand and use the mode and range to
describe sets of data
Level 3 gather information
construct bar charts and pictograms, where the
symbol represents a group of units
use Venn and Carroll diagrams to record their
sorting and classifying of information
extract and interpret information presented in
simple tables, lists, bar charts and pictograms
Level 2 sort objects and classify them using more than one
criterion
understand vocabulary relating to handling data
collect and sort data to test a simple hypothesis
record results in simple lists, tables, pictograms and
block graphs
communicate their findings, using the simple lists,
tables, pictograms and block graphs they have
recorded
* Part of the criteria are covered | 677.169 | 1 |
Precalculus : Schaum's Outline - 2nd edition
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Extended Mathematics for Cambridge IGCSE with CD-ROM
This third edition provides full coverage of the most recent Cambridge IGCSE syllabus in a highly accessible way. It also comes with a free CD, which includes additional exam style questions, interactive exercises and revision tips. We are working with Cambridge International Exa... read full description below.
Description of this Book
This book meets the needs of all students following the Cambridge International Examinations (CIE) syllabus for IGCSE Extended Mathematics. Updated for the most recent syllabus it provides complete content coverage with thousands of practice questions in an attractive and engaging format for both native and non-native speakers of English. The book is easy-to-use with an accessible format of worked examples and practice questions. Each book is accompanied by a free CD which provides a wealth of support for students, such as hundreds of additional homework questions, self-assessment checklists, revision and examination tips, and examiner comments. An accompanying Teacher's Guide and Revision Guide are also available. We are working with CIE to obtain full endorsement of this new edition. | 677.169 | 1 |
Learning Exercise
This assignment was created by Nicole McGlashan of Huron High School, Huron, South Dakota. It describes a self-directed activity in which students discover the nature of the transformation of a function's graph that occurs when the function itself is transformed.. Included in the assignement are links to the National Library of Virtual Manipulatives for Interactive Mathematics and Larry Green's interactive website.
After having completed this lesson the student should be able to determine the initial graph of a function and be able to determine the transformations of its graph that result from transformations of the function.
Text of Learning Exercise: | 677.169 | 1 |
97808058179 Nature of Mathematical Thinking (Studies in Mathematical Thinking and Learning Series)
Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject.
The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat | 677.169 | 1 |
Get the grade you want in algebra with Gustafson and Frisk's
Algebra can be like a foreign language. But one text delivers an interpretation you can fully understand. Building a conceptual foundation in the "language of algebra," iNTERMEDIATEALGEBRA, 4e provides an integrated learning process that helps you expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Packed with real-life applications of math, it blends instructional approaches that include vocabulary, practice, and well-defined pedagogy with an emphasis on reasoning, modeling, communication, and technology skills.
Get a good grade in algebra with Gustafson and Frisk's BEGINNING ANDLarson IS student success. INTERMEDIATEALGEBRA owes its success to the hallmark features for which the Larson team is known: learning by example, a straightforward and accessible writing style, emphasis on visualization through the use of graphs to reinforce algebraic and numeric solutions and to interpret data, and comprehensive exercise sets.
Designed for first-year developmental math students who need support in intermediatealgebra, the Fourth Edition of IntermediateAlgebra owes Student Support Edition continues
KEY MESSAGE: Elayn Martin-Gay's developmental math textbooks and video resources are motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues her focus on students and what they need to be successful. Martin-Gay also strives to provide the highest level of instructor and adjunct support.
Elementary & IntermediateAlalgebra concepts and put the content in context. The authors use a three-pronged approach (I. Communication, II. Pattern Recognition, and III. Problem Solving) to present the material and stimulate critical thinking skills.
Miller/O'Neill IntermediateAlgebra is an insightful text written by instructors who have first-hand experience with students of developmental mathematics. The authors introduce functions in Chapter 3 and do a very thorough treatment, devoting the entire chapter to the concept of functions. With such a solid foundation to build from, students will experience greater success when they encounter other function-related topics in later chapters, such as polynomial functions; quadratic functions; radical functions; and others. The authors have crafted the exercise sets with the idea of infusing review. In each set of practice exercises, instructors will find a set of exercises that help students to review concepts previously learned, and in this way, students will retain more of what they have learned. | 677.169 | 1 |
Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanationsThe CliffsStudySolver workbooks combine 20 percent review material with 80 percent practice problems (and the answers!) to help make your lessons stick. CliffsStudySolver Algebra I is for students who want to reinforce their knowledge with a learn-by-doing approach. Inside, you'll get the practice you need to tackle numbers and operations with... more... | 677.169 | 1 |
Academic Quality and Standards Unit
University of Bolton
Module: Engineering Principles by Zubair Hanslot & P. Myler
Description and Purpose of Module
To introduce learners to a range of core principles and techniques in Mechanical Engineering by the promotion of problem solving skills and methods.
Indicative Syllabus Content
Mathematical methods – Appreciate and use algebra Transformation of formulae. Solution of basic equations (polynomial order <=2) – factorisation, use of formulae and illustration by graphical means. To sketch and use graphs – Predict the behaviour of single valued functions. Linear, Polynomials, Exponential, Non-linear to linear transformations. To solve problems using trigonometry – Appreciate the use and application of trigonometry Solution of triangles, Compound angle formula. Statistical techniques – Appreciate trends and sources of inaccuracies in measured/sampled data. Binomial expansion, Mean, median and mode, Normal, Poisson and Binomial distributions, Probability and its laws, Regression of correlation. To learn the basic use of vectors – Promote spatial awareness by standardisation Concept of a vector – scalar and vector quantities; Vector algebra and resolution of vectors into rectangular co-ordinates, Scalar and vector products. Moment of a force and angular velocity. Forces and stress – Vector methods to static problems Co-planar and concurrent forces; Moment of a force and couples. Newton's Laws. Loading Types: Force, Moments, Torque's, Traction, Pressure using rods, beams and bars (structural elements). Condition for static equilibrium. Resultants and equilibrium of concurrent and non-concurrent force systems. Simple pin jointed frameworks; Use of calculus – Appreciate the effect of changing one quantity with respect to another Concept of differentiation. Differentiation of basic functions. Definitions of linear displacement, velocity and acceleration. Equation of linear motion with constant acceleration. Velocity-time graphs. Definitions of angular displacement, velocity and acceleration. Equations of angular motion with constant acceleration. Relationship between linear and angular motion Numerical differentiation and use of spreadsheets in differentiation. Integration – Appreciate the effect of reversing the process of differentiation. Used to find areas under curves. Concept of integration as reverse of differentiation. Integration of basic functions. Definite and indefinite integration. Integration as area under a graph. Numerical integration. Complex numbers – To extend the simple number system in order to include complex numbers and solve related problems. Appreciate the concept of a complex number; Notation, Cartesian, polar and exponential forms. Arithmetical operations. To analyse simple stress and strain concepts – To appreciate the strength of materials and its definition Direct stress and strain. Hooke's Law and Young's Modulus of Elasticity. Tensile strength and factor of safety. Thermal expansion Effects of thermal strain. Shear stress and strain. Modulus of rigidity. General dynamics – Appreciate the force exerted upon and by moving bodies Definition of basic dynamic terms and relationships between dynamic characteristics; Definitions of mass, force weight momentum. Newton's Laws of Motion. Relationship between force and linear acceleration. D'Alembert's principle and free body diagrams. Relationship between torque and angular acceleration. Moment of Inertia and radius of gyration. Centripetal acceleration. Centripetal and centrifugal forces. Work and energy – Analyse work and forms of energy with its conservation Definition of work. Equivalent work/energy. Work done by a force and a torque. Power transmitted by a force and a torque.
Learning, Teaching and Assessment
Delivery of this module will concentrate on promoting problem solving skills using known and accepted mathematical techniques and scientific principles. The delivery will be structured as follows: Formal lectures constitutes to the delivery of the specified curriculum 42 Tutorials and problem solving support in order to reinforce the above delivery 20 Laboratory sessions used to determine the limitations of scientific principles of the syllabus 8 Assignments specific to laboratory sessions 40 Two phase tests in order to assess previous unseen questions that are similar to the ones illustrated in the problem solving sessions 4 Self directed learning specific to the syllabus content 86 200 specific problems using appropriate analytical techniques Appreciate the application and limitation of the theory used. Assess the sensitivity of the obtained results/solutions/
Solve problems associated with Mechanical Science using pre-prepared data and appropriate analytical techniques. Explain approximations used and its effect e.g. real life measured inertia values compared to mathematically derived values. Investigate the effect on the solution by changing various parameters and appreciate the general trend e.g. Calculus exact and approximate gradients at various points on a curve.
2.
Apply different theories presented in this module. Interpret the problem posed and generate a sequence of tasks necessary to solve the problem.
Demonstrate theoretical knowledge by a laboratory based experiment or case study, based upon measurements and calculations. Illustrate the general sequence and carry them out e.g. Production of free body diagram and application of Newton's and D'Alembert's principle.
3.
Conduct an experiment in a laboratory environment and be able to manipulate the generated/given data.
Extract and present data in the form of a technical report.
4.
To apply mathematical concepts to other situations.
Use mathematical and numerical techniques to solve a range of problems.
Assessment
Your achievement of the learning outcomes for this module will be tested as follows: | 677.169 | 1 |
The ideal review for your collegeTough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's. More than 40 million students have trusted is the Primer level.
The Schaum Note Speller has the unqualified testimonial of thousands of teachers who pronounce it 'The Best.' Musical facts, beginning with line and space numbers are taught. Students learn by doing, since this book is in workbook form. This saves valuable lesson time, and immediately shows any mistakes in the beginner's thinking.
Facing Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Solved Problem book helps you cut study time, hone problem-solving skills, and achieve your personal best on exams! You get hundreds of examples, solved statistics ...
Study faster, learn better, and get top grades Modified to conform to the current curriculum, Schaum's Outline of Probability, Random Variables, and Random Processes complements these courses in scope and sequence to help you understand its basic concepts. The book offers extra practice on topics such as bivariate random variables, joint distribution functions, moment generating functions, Poisson processes, Wiener processes, power spectral ...
The ideal review for your probability and statistics course More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in this field, Schaum's Outline of Probability and Statistics covers what you need to know for your course and, more important, your exams. Step-by-step, the authors walk you through coming up with solutions to exercises in this topic.The ideal review for your trigonometry course More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by a renowned expert in this field, Schaum's Outline of Trigonometry covers what you need to know for your course and, more important, your exams. Step-by-step, the author walks you through coming up with solutions to exercises in this topic. 611 problems solved
This ideal review for your electrical engineering course, with coverage of circuit laws, analysis methods, circuit concepts, and more More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum's Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved ... | 677.169 | 1 |
Discrete Mathematics
Part I of How to Think Like a Mathematician by K. Houston:
Study skills for mathematicians
1 Sets and functions
2 Reading mathematics
3 Writing mathematics I
4 Writing mathematics II
5 How to solve problems
If you are adventurous, you may further wish to browse both or either of
the following.
Part III of How to Think Like a Mathematician by K. Houston:
Definitions, theorems and proofs
14 Definitions, theorems and proofs
15 How to read a definition
16 How to read a theorem
17 Proof
18 How to read a proof
19 A study of Pythagoras' Theorem | 677.169 | 1 |
Intermediateussy and Gustafson's fundamental goal is to have students read, write, and talk about mathematics through building a conceptual foundation in the language of mathematics. Their text blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, communication, and technology skills. With an emphasis on the "language of algebra," they foster students' ability to translate English into mathematical expressions and equations. Tussy and Gustafson make learning easy for st... MOREudents with their five-step problem-solving approach: analyze the problem, form an equation, solve the equation, state the result, and check the solution. In addition, the text's widely acclaimed study sets at the end of every section are tailored to improve students' ability to read, write, and communicate mathematical ideas. The Third Edition of INTERMEDIATE ALGEBRA also features a robust suite of online course management, testing, and tutorial resources for instructors and students. This includes iLrn Testing and Tutorial, vMentor live online tutoring, the Interactive Video Skillbuilder CD-ROM with MathCue, a Book Companion Web Site featuring online graphing calculator resources, and The Learning Equation (TLE), powered by iLrn. TLE provides a complete courseware package, featuring a diagnostic tool that gives instructors the capability to create individualized study plans. With TLE, a cohesive, focused study plan can be put together to help each student succeed in math. Learn math the easy way with Tussy and Gustafson's INTERMEDIATE ALGEBRA! Study sets at the end of every chapter will improve your ability to read, write, and communicate mathematical ideas. Difficult concepts are made clear with a five-step approach to problem-solving: analyze the problem, form an equation, solve the equation, state the result, and check the solution. Prepare for exams with numerous resources located online and throughout the text such as live online tutoring, tutorials, a book companion website, chapter summaries, self-checks, practice sections, and reviews. Take advantage of the accompanying Video Skillbuilder CD-ROM that will save you class preparation time through video lessons, web quizzes, and chapter tests. | 677.169 | 1 |
More About
This Textbook
Overview
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical | 677.169 | 1 |
Basic Mathematical Skills with Ge CD-ROM is a self-paced tutorial specifically linked to the text and reinforces topics through unlimited opportunities to review concepts and practice problem solving. The CD-ROM contains chapter-and section-specific tutorials, multiple-choice questions with feedback, and algorithmically generated questions. It required virtually no computer training on the part of students and supports IBM and Macintosh computers. In addition, a number of other technology and Web-based ancillaries are under development; they will support the ever-changing technology needs in developmental mathematics. | 677.169 | 1 |
Index AlgebraDiscrete mathematics is a blend of many different elements of logic, combinatorics and graph theory. I hold a Master's in Math Education and have coached many students through various Discrete math courses. Let me help you reduce your math anxiety | 677.169 | 1 |
It's very hard to base a question's level on class level. Intro to Analysis (300 level) only requires Calc II at my University. At my previous school Elementary Linear Algebra was a 200 level class and here it is a 300 level class. I can imagine someone coming in to ask a question regarding a basic convergence proof would get down voted/ignored here and it is an "upper-level undergraduate" question.
The people here either need to relocate to a place with a more daunting name like /r/mathematicians or just deal with having some basic questions asked... it's part of having the /r/math sub.
I was thinking the same thing this afternoon, but what I was envisioning was just an app with a ton of theorems and propositions and their proofs, maybe with a highlight of the different techniques used in the proof. It isn't that I was to memorize proofs, but when I have dead time it'd be nice to have some math to study.
The fact is you're going to end up taking some kind of Intro to Analysis course or something when you transfer so I would just get what you can out of the book and you'll be way ahead of the rest of the class. At my university, CSU, the Intro to Analysis class is considered the hardest undergrad math course even according to people who take Advanced Calculus (417) and then go back down to Intro to Analysis (317).
My advice is to focus on proof techniques over theorems. You'll relearn all the theorems, but being comfortable with the techniques is what will make exams and understanding what is happening easier.
I'm not complaining about the charts or anyone's theories. I just wanted to bring up the importance of the other threads that spawned in other parts of Booker's life. Obviously the game as we saw it utilizes some cool concepts of waveform superimposition and recurrence in random walks, but part of the beauty of the game, which it basically shouts at you, is that the whole story is minute in comparison to everything. Not complaining, just a point of discussion :).
But why can't one of those universes be where he wakes up at the end? These charts are great but I think they artificially limit the breadth of the story. Obviously there isn't much to talk about in them but it feels like their existence gets ignored.
Songbird's story, and more about the handymen.... they all seemed so tragic... the voxaphone from the handyman's wife was one of the most touching parts of the game :(. Obviously we need more of the Luteces too.
That's not exactly true, they killed all Brookers who chose to go to the baptism. Who remains are the Brookers who learned to cope or didn't take part in Wounded Knee. I think of it as the ultimate baptism.. it wiped away all the really bad versions of himself. I think of it like rolling back a code branch or pruning a tree.
Not me, but my employer is an executive coach. He's a Doctor of Theology that executives hire to coach them through ethical decisions. Another one is my best friend who is an "industrial designer," he designs things like the backs of tablets, heatsinks on RAM, and other kinds of enclosures.
As a small token of our appreciation, we are offering you a free EA PC game download on Origin*. Mayors who have authenticated their copy of SimCity on Origin by March 25 can select a free game through a redemption portal inside the Origin desktop client later this week. We'll be opening up the redemption portal country-by-country so some of you may see it a little sooner than others. The portal will be live worldwide for everyone to select their game by March 22.
One of my cities is similar but I stared it with power, water, and sewage, but it's all residential and I shut off utilities around 100k people. My tax rate is 1% (can't set 0% tax without a city hall which costs 200 an hour), I have tons of homeless because of rolling house abandonment, fires burn constantly and criminals are everywhere. But things keep getting bigger density, everyone is happy (80% - 96% approval), I make money and all I have to do is bulldoze anything that burns down or is abandoned, (current pop 316k).
But it isn't fun and all it proves is that if you want to play "bulldozer whack-a-mole" and run a horrible city in the game you can. But you can have more fun with more complex cities (but it does feel a bit empty :().
I very highly double the game programmers are the same network engineers who designed the infrastructure, and developers who build the DRM. In fact with how broken everything is, I feel like they were TOO siloed because there is clearly a lack of communication between different parts. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
This textbook is a new introduction to linear algebra for students who have completed the first year of calculus. In the spirit of modern instruction, this elementary presentation of the important ideas in linear algebra emphasizes conceptual understanding, developing applied examples, and working with realistic numerical data before introducing formal mathematical definition and operations. This text emphasizes geometric, symbolic, and numeric presentations of the subject. The first two chapters cover linear phenomena in both numeric and geometric settings. The symbolic manipulation of vectors and matrices is then introduced as a tool for the study of specific problems. Many examples, student exercises, and group project ideas are included.
Synopsis:
The objective of this text is to bring a different vision to this course, including many of the key elements called for in current mathematics-teaching reform efforts | 677.169 | 1 |
A good introduction to school algebra -- one that is worth the student's time and effort -- should leave the student believing that algebra is exactly as she knows it should be. The author has taught... More > school mathematics to grades 4 through various years of calculus. In doing so, he has seen children display intellectual sophistication that they are supposed to be too young to have. This text does not assume such sophistication, but provides opportunities for it to appear and be enjoyed. The author's deeply held belief that the student, although less experienced, is a peer in the quest for mathematical truth has produced a book respectful of the student's intellect, curiosity, wonder, and humanity. The text includes no fewer than 985 problems. Answers to all problems and full solutions to many are provided in the Appendix. Most of these problems are practice, but there are some that go deeper than mere practice and typically ask the student for a proof or a reasoned explanation.< Less
Most students have a blend of emotions while dealing with Algebra. Talking about x and y, unknowns and equations, is exciting, and equally confusing. This is not just our premise, but this is based... More > on feedback / direct inputs we have received from the student, teacher and parent community. We started a project to address this conceptual gap.We started stringing together a set of concepts followed by a problem set using the preceding texts. This effort left us with a skeletal structure of concepts in Algebra which progresses from basics to through to advanced topics. This formed the basis of our work on "Elementary Algebra". We sincerely hope that the student is able to get a good grasp of the subject and the techniques after working with the contents of this book.< Less | 677.169 | 1 |
Course MAT201
Calculus III (Multivariable Calculus)
A continuation of MAT103/104, the third semester in the calculus sequence gives a thorough introduction to multivariable calculus and mathematical methods needed to understand real world questions involving quantities changing over time in 3-space. Topics include limits, continuity and differentiability in several variables, extrema, Lagrange multipliers, Taylor's theorem, multiple integrals, integration on curves and surfaces, Green's theorem, Stokes' s theorem, divergence theorem. Emphasizes concrete computations over more theoretical considerations. However, this course demands that students move beyond thinking of mathematics as a set of rules and algorithms to memorize, and begin to approach problems with greater independence and maturity. Exams test for thorough conceptual understanding and computational fluency in standard cases. Although demanding, the exams do not typically involve any proofs, and there is little emphasis on exceptional cases. Offered both Fall and Spring. Prerequisite: MAT104 or equivalent.
The first part of the course introduces basic objects in space: lines, planes, curves, (quadric) surfaces, and basic properties like arc length, surface area and volume.
The second part moves on to quantities that change with position in 3-space, like temperature or population density, which can be described by functions of several variables. We study their graphs, level sets, rates of change (partial derivatives) and their extreme points (maxima/minima) using Lagrange multipliers and Taylor's theorem.
The third part is devoted to vector fields, quantities that change with both position in space and with time. Think of how storms move, how radio signals make cell phones work or how blood flows. Although we do not explicitly study such applications, we lay the mathematical foundation for more advanced courses in science, engineering, and economics. The course ends with the theorems of Green, Gauss, and Stokes.
Description of classes
Classes meet 3 times per week, for 50 minutes. Sections are generally offered MWF at 10, 11 and 12:30 in both semesters.
The course is organized into small sections of 20 to 30 students. There is one course head who coordinates with all the instructors to write the exams. All students have the same homework assignments and take the same midterm and final exam. The midterm and final count for the bulk of the course grade, typically about 70%. These exams are graded by all the instructors and graduate student AI's together to ensure uniformity across all sections. Typically there are two to four take-home quizzes, the same for all sections. Homework and quizzes together usually account for about 30% of the course grade.
In order to do well in the course, we anticipate that most students will need to spend approximately ten hours per week reading the text, reviewing class notes, solving homework problems and working through lots of extra practice problems to prepare for quizzes and exams. The course will be quite fast-paced and it is essential to work steadily throughout the semester. Frequent feedback will be given to help students keep up and monitor progress.
The first half of MAT201 generalizes MAT103 to higher dimensions, and the second half generalizes MAT104.
Students who have already taken MAT175 should not sign up for MAT201 because there is too much overlap between these two courses. MAT175 is intended for students who will not take futher mathematics courses at Princeton; in rare cases it may be possible for a highly motivated student who received a grade of at least B+ to attempt MAT202 afterwards, but he/she should expect to work extremely hard in order to succeed.
Who Takes This Course
Most students in this course are incoming freshmen or sophomores who consider majoring in one of the sciences or engineering. More mathematically inclined economics majors will take this course along with MAT202 (instead of MAT175). It gives a solid introduction to multivariable calculus suitable for most students who want to use mathematics as an analytic tool in later studies in other fields. Although it is not a prerequisite, many students in the course will have had a more basic multivariable calculus course in high school.
Most students in the course are freshmen; in the fall they are students who got a 5 on the BC exam in high school (or its equivalent). In the spring, they are mostly continuing from MAT104.
Students who took AB calculus only should take MAT104 instead. There is one possible exception to this rule: students with a 5 on the AB exam and a very strong interest in math as a major along with a math SAT score of at least 750 can consider taking MAT215 or MAT214 instead. This is rather rare, and such students should consult the math placement officer.
Students who consider a major in physics or applied math should consider MAT203 or MAT215 instead if they have a 5 on the BC exam (or equivalent) and a math SAT score of at least 750.
Future math majors usually learn multivariable analysis (calculus) in MAT218 instead (after MAT215 and MAT217). Some, especially those who are more interested in applied math opt for MAT203.
Some economics majors take MAT175 instead for a much more basic treatment of some of the ideas in MAT104, MAT201 and MAT202 in one semester.
A very solid knowledge of single-variable calculus and precalculus is needed: how to analyze and graph functions, how to compute and interpret derivatives, how to interpret, set up, and calculate definite integrals with speed and accuracy. An interest in thinking rigorously about problems involving space and time is also needed.
If your background is weak or rusty consider MAT104 to get an excellent review of the knowledge assumed in this course.
Keep in mind that a score of 5 on the BC calculus exam is minimally equivalent to MAT104, probably equivalent to a grade of C. As a result, many students who scored a 5 on the BC calculus exam or took a similar course in high school (and did well) opt to start in MAT104 and find it to be quite challenging. Although many of the topics in MAT104 are somewhat familiar after a BC calculus course, the depth of coverage and mastery of the subject required here is much greater, with more emphasis on independent thinking. Additional topics that are not covered in most BC calculus courses are also included.
Note that a score of 7 on the IB MathHL exam (not SL!) or an A on the British A-levels exam is treated as equivalent to a 5 on the BC exam here and at many other universities. These scores indicate that MAT201 is a reasonable starting point for you.
If in doubt, sign up for MAT201 and be prepared to re-evaluate during the two weeks of classes.
You should probably take MAT201 and switch down after a couple of weeks, if necessary. Taking MAT175 limits your options and not every program accepts it as a substitute for MAT201; you should not take it if you may later need further math courses at Princeton. Also, keep in mind that these courses are not generally offered at the same time, so plan your schedule carefully to leave room for MAT175 if you think you may want to switch.
Working problems from these sample quizzes and exams can give you a good idea of the expectations and content in this course as you think about which course is right for you. Just reading the questions or the solutions can be very misleading however. Try the problems yourself!
I already took multivariable in high school, do I have to take this course?
Most students in MAT201 have had some multivariable calculus and/or linear algebra before, but rarely with the same depth and thoroughness. If you need the course for upper division courses in your major, then you are probably better off to take MAT201 even though some material will be review.
Not convinced? Take the sample final. Can you do any of the problems? For most students, the answer will be no. Review your old notes and try again. Can you do at least 60% of the exam?
In rare cases, the placement officer will decide that your prior work is indeed equivalent to MAT201 at Princeton. It will be helpful if you can bring your graded exams from the course you took to show the placement officer. He/she may also require you to take an exam to demonstrate your knowledge.
You might consider MAT203 or MAT218 instead (if you take MAT215 and MAT217 first) but these courses are not for everyone -- they require an intense commitment and interest in math for its own sake, not just fulfilling a requirement.
Can I take MAT201 and MAT202 in the same semester?
It is not impossible, but we do not recommend it. It makes midterm week particularly unpleasant, but if you have a very good reason for it and you are a very strong student, it can be done. It will likely mean that you will get a lower grade in one of them that you would otherwise have done.
How much work is this course?
Most math courses require a steady time commitment. We expect that the weekly problem sets will take at least three hours to complete, although this can vary quite a lot depending on your background and goals. To do well on math exams, you need to work through a lot of extra problems. All in all, you should be ready to spend up to ten hours per week working outside of class.
If I think MAT201 is too hard, what should I do?
You may have a couple of options, depending on which courses you have already taken here at Princeton and depending on your major. You may consider switching into MAT175 but only if you are completely sure that you don't need to take any further math courses and that your program will allow you to substitute MAT175 for MAT201. If you want to major in engineering, then your only option is to consider dropping back to MAT104 to get a thorough review of all the material assumed in MAT201. As a future BSE major, starting in MAT104 will not throw you off-track, and taking the time to strengthen your foundations can really pay off in the long run.
Try an old final exam in MAT104. Can you do at least half of the problems correctly? (Try the problems -- don't just read the questions!) If you do need to switch down to MAT104 because your knowledge of one-variable calculus is insufficient, then you should decide this as quickly as possible because there is very little overlap between the first half of MAT201 and MAT104. If you wait too long, it will be very difficult to catch up and do well in MAT104.
Peer tutoring can be arranged through your residence college, and there is also help available at the McGraw Study Halls. Talk to your instructor!
If I think MAT201 is too easy, what should I do?
Have you had a quiz yet? You may be in for a surprise. Homework and the first couple of weeks of class can be misleading since the first few topics are not too difficult and the homework problems are quite routine compared to the exam questions. Try a sample quiz or midterm for this course. Remember -- don't just read the question. See if you can produce correct solutions to most of the problems in the allotted time.
If you are also taking PHY103, you might consider just enjoying the fact that MAT201 is too easy. The combination of a demanding physics class and a demanding math class has been responsible for quite a few academic distress stories at Princeton.
I need both MAT104 and MAT201 for my major. After checking the math placement information, I think MAT201 is probably the right course for me, but I don't qualify for AP credit for MAT104. Do I have to take MAT104 or can I sign up for MAT201 instead?
Be cautious. Students often underestimate the difficulty of MAT104 and of MAT201 because many have seen some of the techniques taught in the first few weeks of these courses. Consider the information in the previous two questions as you think about your decision.
If you are really sure that you belong in MAT201, you can sign up for it. If you pass MAT201 in your freshman year, you will automatically receive AP credit for MAT104. Just be ready to re-consider and switch down to MAT104 early on if necessary since there is very little overlap with the first half of MAT201 and the material in MAT104.
If I want to switch courses, what should I do?
Details of departmental drop/add/swap procedures and information about who to contact for advice about courses can be found on the undergraduate home page. But don't delay -- If you are going to switch, do it soon!
I would like to switch sections within MAT201, what should I do?
If you have a time conflict, there is usually no problem. If you want to switch to another section at the same time, be prepared for a possible refusal --- the instructor may not have room for another student. Details of departmental drop/add procedures and information about who to contact for advice about courses can be found on the general Math FAQ page. But don't delay -- if you are going to switch, do it soon!
I can't fit this course into my schedule. Can I take this course for Princeton credit at another university?
Yes, but it may be difficult to find an equivalent course. Many multivariable courses at other universities cover only about half of 201. Check out our summer course approval procedures.
I have more questions that are not answered here. What should I do?
First, check the undergraduate home page for more information about how our courses work in general and about who to contact if you need to discuss your situation with someone from the math department. Also: representatives from the math department will be available at freshman registration. | 677.169 | 1 |
These authors understand what it takes to be successful in mathematics, the skills that students bring to this course, and the way that technology can be used to enhance learning without sacrificing math skills. As a result, they have created a textbook with an overall learning system involving preparation, practice, and review to help students get the most out of the time they put into studying. In sum, Sullivan and Sullivan's Precalculus: Enhanced with Graphing Utilitiesgives students a model for success in mathematics. This is just the standalone book.
decent book need for class so not much i can review for it comes with a lot
decent book need for class so not much i can review for it comes with a lot of cds though!!!
decent book need for class so not much i can review for it comes with a lot of cds though!!! decent book need for class so not much i can review for it comes with a lot of cds though!!! decent book need for class so not much i can review for it comes with a lot of cds though!!!
Actually a really nice book
i get this book for a summer course i am taking. i didn't want to spend $200 on a book i was only going to use for 6 weeks so i found it on half.com. the book has a lot of examples that help you learn. what i also liked about it that you can register with mathxl and you can do all homework on it and it grades it for you. and i'll give you lots of sources to get help. and you can do the problems as many times as you want until you get the grade you want or until you learn it. it's a great tool. i strongly suggest it. the only reason i'm giving it a good rating is because it was so expensive. | 677.169 | 1 |
The following is a summary of main duties for some occupations in this unit group:
Mathematicians conduct research to extend mathematical knowledge in traditional areas of mathematics such as algebra, geometry, probability and logic and apply mathematical techniques to the solution of problems in scientific fields such as physical science, engineering, computer science or other fields such as operations research, business or management.
Statisticians conduct research into the mathematical basis of the science of statistics, develop statistical methodology and advise on the practical application of statistical methodology. They also apply statistical theory and methods to provide information in scientific and other fields such as biological and agricultural science, business and economics, physical sciences and engineering, and the social sciences.
Actuaries apply mathematical models to forecast and calculate the probable future costs of insurance and pension benefits. They design life, health, and property insurance policies, and calculate premiums, contributions and benefits for insurance policies, and pension and superannuation plans. They may assist investment fund managers in portfolio asset allocation decisions and risk management. They also use these techniques to provide legal evidence on the value of future earnings.
Jobs for Mathematicians, Statisticians and Actuaries in Saguenay--Lac-Saint-Jean Region | 677.169 | 1 |
MAZ505: AlgModel (2013-2014)
Major Concepts/Content: Algebraic Modeling will help students understand the connection between math and their daily lives. Students will explore Algebra 1 topics such as linear, quadratic, exponential and piecewise functions by modeling real world situations. Students will identify key characteristics, represent problems algebraically and graphically, determine lines/curves of best fit and make predictions. Concepts and solutions are presented in non-threatening, easy-to-understand language with numerous examples to illustrate ideas. Whether the student will go on to study early childhood education, graphic arts, automotive technologies, criminal justice or something else, the student will discover that the practical applications of mathematical modeling will continue to be useful well after they have finished this course.
Major Instructional Activities: This course is designed to help students make connections between algebra and real world applications through activities, modeling and extensive conversations. Students will be expected to explore real world data, make conjectures about different situations and communicate their thoughts in a variety of ways. Students will become proficient in a variety of technologies including: graphing calculators and software for graphing /modeling, word processing, spreadsheet processing and presentation software.
Major Evaluative Techniques: Students will demonstrate their knowledge through tests, hands-on demonstrations, technical reports, projects, case studies, and reflections.
Course Objectives: Throughout this course, students will create and use mathematical models employing algebraic modeling techniques with the following mathematical concepts | 677.169 | 1 |
Algebraic Geometry Teacher Resources
Find Algebraic Geometry educational ideas and activities
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In this Algebra I/Geometry/Algebra II worksheet, students solve problems that reflect the types of assessment items found on the Regents Examination for the state of New York. The seventy-one page document contains a combination of thirty-four multiple choice and free response test items along with samples of student work, rubrics, and subject matter alignment. Answers are not included.
Students explore careers that require math knowledge and solve real life math problems. As a class, they compare and contrast classroom math to real life math and explore the links between algebra, geometry and math skills used in school and in a career. In pairs, students complete worksheets. They play a quick response game where they list five ways a given job uses math.
Students assess how algebra, telescopes, space exploration and optics are so important in astronomy. They encounter studies on the Hubble Space Telescope, Hubble Deep Field and how algebra helps to determine the effects of contamination on Hubble's optics. Students are introduced to the development of the Next Generation Space Telescope.
Help 9th graders identify lines, points, rays, and planes in geometry. They practice identifying, measuring, and drawing angles of different degrees. This is a fundamental lesson to help students learn the building blocks of geometry.
Study geometry through the concept of quilt design. High schoolers examine the geometric shapes in various quilts and then create their own quilts using geometric shapes that fit together. In the end, they write a paragraph to describe their quilt pattern.
Students explore properties of triangles. In the geometry lesson, students construct the centroid, circumcenter, and the orthocenter of a triangle. The dynamic nature of Geometer's Sketchpad allows students to discover important properties regarding Euler's line. Additionally the lesson considers a proof of the Pythagorean Theorem and investigation into Fermat's point.
Students explore the concept of iteration, recursion, and algebra to analyze a changing fish population. In this iteration, recursion, and algebra lesson plan, students explore the effects a change in a parameter has on a graph. Students use an applet to change parameters of a fish population and see the effect on the graph.
Students relate miniature golf to reflection of an image. In this algebra instructional activity, students collect and graph data as they study linear equations. They apply properties of graphing to solve real life scenarios.
Young scholars identify he proportion of a cereal box. In this algebra lesson, students define the relationship between patterns, functions and relations. They model their understanding using the cereal box.
Students investigate linear equations through models. In this algebra instructional activity, students investigate solving one and two step equations. Review solving a basic equation before starting this assignment.
Students discuss what good presentation looks like. In this geometry lesson, students discuss the 7 important steps required to be a good presenter. They start with their names and what they will be discussing and end with a thank you to all who helped with the creation of their work. They may work in groups. | 677.169 | 1 |
itioning between two worlds, students in the middle grades (4-9) are no longer elementary students but are not quite ready for the challenges of secondary school. The state departments of education are beginning to recognize that the preparation of teachers for these students must change. Teaching and Learning Middle Grades Mathematics is the ideal text for future teachers who are completing their pre-service instruction. Through readings, lessons, sample middle grades exercises, and more, future teachers learn to address the teaching and ... MORElearning of algebraic and geometric thinking at the level appropriate for middle grades students. The lessons in this text follow a popular collaborative teaching method used in middle schools called Launch, Explore, Share and Summarize that involves very little lecturing, a lot of group work, and class discussions. Teaching and Learning Middle Grades Mathematics will serve as a life long resources to students, as each lesson is filled with student pages which are worksheets that can be modified for use in actual middle grades classrooms. The text comes packaged with a CD-ROM that will be a valuable resource, containing professional readings that correlate directly to the lessons in the text. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
A plain-English guide to the basics of trig
From sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English, offering lots of easy-to-grasp example problems, and adding a dash of humor and fun. It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers.
Mary Jane Sterling (Peoria, IL) has taught mathematics at Bradley University in Peoria for more than 20 years. She is also the author of the highly successful Algebra For Dummies (0-7645-5325-9).
Synopsis:
Get up to speed quickly with worked-out problems
Understand the how and the why of trigonometrySynopsis:
"Synopsis"
by Ingram, | 677.169 | 1 |
TRIGONOMETRY CHALLENGE is designed to supplement your classroom and textbook instruction. The topics included in the program are: The Pythagorean Theorem, Degree and Radian Conversion, Using the Sine Function, Using the Cosine Function, Using the Tangent Function, The Inverse Functions, The Law of Sines, The Law of Cosines. The activities are constructed from ramdom variables. Student work is graded instantly. Grades can be printed on "certificates" or stored on diskettes. The program is simple to install and use. An unlimited use site license is $159.00. Licensed sites can optionally allow students and teachers to use a copy of the program on their home computers.AC Circuits Challenge - This interactive computer program consists of several circuit analysis activities.This interactive computer program consists of several circuit analysis activities. Realistic troubleshooting activities are also included involving resistors,...
Basic Circuits Challenge - Basic Circuits Challenge consists of a set of fifteen activities to help you teach basic electrical concepts.Basic Circuits Challenge consists of a set of fifteen activities to help you teach basic electrical concepts. Exercise Titles: Electric...
DC Circuits Challenge - This interactive computer program consists of several circuit analysis activities.This interactive computer program consists of several circuit analysis activities. Realistic troubleshooting activities are also included involving resistors,...
Ohmmeter Challenge - Ohmmeter Challenge is designed to help you teach students to analyze wiring and troubleshoot circuits using digital ohmmeters.Ohmmeter Challenge is designed to help you teach students to analyze wiring and troubleshoot circuits using digital... | 677.169 | 1 |
Driving Directions
Plain text directions to get you to the Department of Mathematics and Computer Science offices are as follows:
From the Pennsylvania Turnpike (Interstate 76)
1. Leave the turnpike at Exit 226, the "Carlisle" exit; stay in the right lane to follow US Route 11 south.
2. Follow US Route 11 approximately 2.5 miles into Carlisle where it becomes North Hanover Street.
3. Continue south on Hanover to its intersection with Louther Street.
4. Turn right (west) onto Louther Street and follow it three and a half blocks.
5. The Math/CS department is in Tome Hall in the Rector Science Complex on the right side of Louther Street.
6. The Math/CS department is on the second floor of Tome hall.
From Interstate 81:
1. Take Exit 47 if on I-81N and make a left at the end of the ramp OR take Exit 47B if on I-81S and make a right at the end of the ramp. You are now on Hanover Street (PA Route 34) heading into Carlisle.
2. Follow Hanover Street approximately 1.5 miles to the sixth traffic light at Louther Street.
3. Turn left (west) onto Louther Street and follow it three and a half blocks.
4. The Math/CS department is in Tome Hall in the Rector Science Complex on the right side of Louther Street.
5. The Math/CS department is on the second floor of Tome hall. | 677.169 | 1 |
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