Mathematical Methods for Physics and Engineering

"This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you."The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later."The book is divided into sections devoted to different topics. Some of them are very short, others are rather long."As organized and directed by I. M. Gelfand for a Mathematical School by Correspondence, the books are intended to cover the basics in mathe­matics. ...As Gelfand himself has stated:"It was not our intention that all of the students who study from these books or even completed the School by Correspondence should choose mathematics as their future career. Nevertheless. no matter what they would later choose, the results of this mathematical training remain with them. For many. this is a first experience in being able to do something completely independently of a teacher." Contents......Page 3 3 Exchange of terms in multiplication ......Page 6 4 Addition in the decimal number system ......Page 7 5 The multiplication table and the multiplication algorithm ......Page 10 6 The division algorithm ......Page 11 7 The binary system ......Page 13 9 The associative law ......Page 16 10 The use of parentheses ......Page 18 11 The distributive law ......Page 19 12 Letters in algebra ......Page 20 13 The addition of negative numbers ......Page 22 14 The multiplication of negative numbers ......Page 23 15 Dealing with fractions ......Page 26 16 Powers ......Page 30 17 Big numbers around us ......Page 31 18 Negative powers ......Page 32 19 Small numbers around us ......Page 34 20 How to multiply am by an. orwhy our definition is convenient ......Page 35 21 The rule of multiplication for powers ......Page 37 22 Formula for short multiplication: The square of a sum ......Page 38 23 How to explain the square of the sum formula to your younger brother or sister ......Page 39 24 The difference of squares ......Page 41 25 The cube of the sum formula ......Page 44 26 The formula for (a + 6)4 ......Page 45 27 Formulas for (a + 6)5, (a + 6)6, . . . and Pascal's triangle ......Page 47 28 Polynomials ......Page 49 29 A digression: When are polynomials equal? ......Page 51 30 How many monomials do we get? ......Page 53 31 Coefficients and values ......Page 54 32 Factoring ......Page 56 34 Converting a rational expression intothe quotient of two polynomials ......Page 61 35 Polynomial and rational fractions in one variable ......Page 66 36 Division of polynomials in one variable: the remainder ......Page 67 37 The remainder when dividing by % - a ......Page 73 38 Values of polynomials, and interpolation ......Page 77 39 Arithmetic progressions ......Page 82 40 The sum of an arithmetic progression ......Page 84 41 Geometric progressions ......Page 86 42 The sum of a geometric progression ......Page 88 43 Different problems about progressions ......Page 90 44 The well-tempered clavier ......Page 92 45 The sum of an infinite geometric progression ......Page 96 46 Equations ......Page 99 48 Quadratic equations ......Page 100 49 The case p = O . Square roots ......Page 101 50 Rules for square roots ......Page 104 51 The equation x^2 + px + q = 0 ......Page 105 52 Vieta's theorem ......Page 107 53 Factoring ax^2 + bx + c ......Page 111 54 A formula for ax^2 + bx + c = 0 ......Page 112 56 A quadratic equation becomes linear ......Page 113 57 The graph of the quadratic polynomial ......Page 115 59 Maximum and minimum values of aquadratic polynomial ......Page 119 60 Biquadratic equations ......Page 121 61 Symmetric equations ......Page 122 62 How to confuse students on an exam ......Page 123 63 Roots ......Page 125 64 Non-integer powers ......Page 128 65 Proving inequalities ......Page 132 66 Arithmetic and geometric means ......Page 135 68 Problems about maximum and minimum ......Page 137 69 Geometric illustrations ......Page 139 70 The arithmetic and geometric meansof several numbers ......Page 141 71 The quadratic mean ......Page 149 72 The harmonic mean ......Page 152 This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

the Need For Improved Mathematics Education At The High School And College Levels Has Never Been More Apparent Than In The 1990's. As Early As The 1960's, I.m. Gelfand And His Colleagues In The Ussr Thought Hard About This Same Question And Developed A Style For Presenting Basic Mathematics In A Clear And Simple Form That Engaged The Curiosity And Intellectual Interest Of Thousands Of High School And College Students. These Same Ideas, This Development, Are Available In The Following Books To Any Student Who Is Willing To Read, To Be Stimulated, And To Learn.

Algebra Is An Elementary Algebra Text From One Of The Leading Mathematicians Of The World -- A Major Contribution To The Teaching Of The Very First High School Level Course In A Centuries Old Topic -- Refreshed By The Author's Inimitable Pedagogical Style And Deep Understanding Of Mathematics And How It Is Taught And Learned.


this Text Has Been Adopted At:
holyoke Community College, Holyoke, Ma * University Of Illinois In Chicago, Chicago, Il * University Of Chicago, Chicago, Il * California State University, Hayward, Ca * Georgia Southwestern College, Americus, Ga * Carey College, Hattiesburg, Ms

Its a great book! You can't deny it! But, if you have more than some experience in algebra, you may want to consider something else. I would have liked it even more if had hard problems from Olympiads.