Book Description

The first and only text of its kind, Mathematics for Elementary School Teachers, 2/e, offers a comprehensive, content approach designed to foster hands-on, discovery-based mathematics instruction.Students first encounter new concepts through hands-on activities in the Explorations Manual, enabling them to construct their own understanding of the material. The text then serves as a resource for further investigation, explanation, and clarification.

Unlike most texts, which present exercises very similar to examples, Bassarear demonstrates how real-life problems are generally complex and often filled with ambiguity. Students learn that there may be more than one way to find an answer—and even more than one answer.

Book Description

This text aims to provide an introduction to the subject of quantum field theory without the complication of introducing its application areas such as elementary particle physics or statistical physics at the same time.
It explains those features of quantum and statistical field systems that result from their field-theoretic nature and are therefore common to different physical contexts. The reader is supplied with practical tools for carrying out calculations as well as a discussion of the meaning of the results.
An approach emphasizing the simplest models is used, progressing to discussion of real systems before mentioning more general and rigorous conclusions. The book is structured around carefully selected problems, which are solved in detail. The central concept is that of effective action (or free energy in statistical physics), and the main technical tool is the path integral, although other formalisms are also mentioned. A knowledge of particle physics phenomenology is not required. T ... Read more

Reviews (2)

Excellent informal QFT intro
You want to know what is Casimir effect, renormalization and Callan-Symanzic Eqn, effective action and path integral. You take a standard QFT course (say, Weinberg or Peskin) and find yourself overwhelmed with peculiarities of Dirac spinors and Lorentz group representations. You feel you are not going anywhere: you are not learning QFT, really! Maybe you are even not a particle physicist after all. Then this book is for YOU! Authors do a great job explaining the essence of QFT (as an interacting theory with an infinite number degrees of freedom) using the scalar field Lagrangian with the quartic interaction as a prime example. It is amazing how far one actually can go with such a model! Each chapter contains an illustrative calculation of a physical quantity (say, the Casimir energy, Ch. 5), with all the details, and without unnecessary complications. One also learns a great deal of the path integral techniques (e.g. instantons), which is extremely important in a variety of fields (QCD, condensed matter, statistical physics, etc). Overall, a highly recommended reading.

A great introductory course
I've looked at many books on quantum field theory and this is without doubt the best introductory work I have found. The Weinberg book jumps in at the deep end, the Kaku book jumps in at about 6 feet deep but this one allows you to at least climb into the pool. It's a rare intelligence to be aware of how to lead one's reader along the learning curve and these authors display it. Typo errors occur at the rate of about one every two pages (did anyone read the proofs?) but they are easily discovered if one follows the math carefully. ... Read more

Book Description

Introductory text for engineers, physicists and applied mathematicians applies mathematics of Cartesian and general tensors to physical field theories, demonstrating them chiefly in terms of the theory of fluid mechanics. Many exercises throughout the text. Index. Preface. Appendixes.
... Read more

Reviews (5)

Not for the weakhearted!
This is one of those pithy classics that one needs to tread through very very carefully. The book is an uphill task, wherein rests its utility and fun. Fluid Mechanics in its simplified diluted version is served in many OTHER textbooks. This one serves it in its raw mathematical glory, and as the author says in the preface of the book, any serious engineer and fluid mechanician must realize that math must be befriended and mastered. The author makes very terse, and powerful introduction to the field. I would recommend a physicist to supplement it with a text by Faber, for Chemical Engineer to study it after the famous BSL (Transport Phenomenon), for a mathematician to pick it on any day, and for everyone in general to approach it with determination required to climb a rocky terrain. (Ah! I guess I would write an even better review if and when I finish reading it:)

Good reference
This book would be good for a reference, however, I would not reccomend it for learning the subject or to supplement a course on fluid mechanics.

Primer
This book comes from the author who is influenced by Clifford Truesdell(pioneer of Rational Continuum Mechanics & Thermodynamics). This book can be a good introductory material to begin study in rational mechanics. However, not so serious students may find it disappointing. One can surely learn some good tensor manipulation skills with application to fluid mechanics.

Too good!
Well, I don't want to go into an endless list of superlatives which this book really deserves. I'd rather point out some of its features. It's terse, sometimes awfully so & therefore, this's not the best book to learn the "basics". Don't expect any elementary physics of fluid flow. I've only read the first half of the book and in those less-than-hundred pages, I've appreciated fluid mechanics much more than I've by any other means. However, I must say that the so-called "indices" notation for vectors and tensors can be extremely frustrating and even confusing. This notation is so extensively used in the book that it can become possibly the only reason to put the book down. The order of presentation is quite nice.

There are few problems to solve which mostly seem to fill in the details of presentation. The last chapter on mass transport is a disappointment, with nothing close to what one would expect in a book of this stature. It is however included only because "it would be unpardonable not to do so, for a book coming from Chemical Engineering dept".

The author says in his preface that the time has come to go beyond the notion that engineers don't need rigorous applied mathematics and he proves his point in every page of his book. It's a pleasure to read and work on, especially the second half of the book. With patience, paper and pencil (lots of them), one can gain a real mastery over the subject. A true graduate-level book!

Gangbusters!
I just couldn't get enough of this book. A real page-turner ... Read more

Book Description

Reviews (5)

Solid Introduction to Metric Spaces and Continuous Functions
Introduction to Analysis by Maxwell Rosenlicht is another bargain from Dover Publications. I used this inexpensive mathematics reprint to help fill in gaps in my background before tackling more advanced mathematics. I found the first 150 pages to be challenging, but manageable. I had less success with the last the last 100 pages.

My college work was limited to applied mathematics, but in recent years I have developed some familiarity with metric spaces, topology, and analysis. (I previously reviewed Metric Spaces by Victor Bryant and Introduction to Topology by Bert Mendelson.)

Throughout his text Rosenlicht emphasizes how the same idea or theorem can be formulated in various ways. I found his approach to be quite helpful in clarifying more abstract representations of key ideas.

The first two chapters review set theory and the real number system and should be familiar to many readers. However, Chapter 3 (Metric Spaces) and 4 (Continuous Functions) are critical and will require substantially more effort. My pace slowed dramatically.

For the reader new to metric spaces, Chapter 3 will likely be challenging, although metric space concepts are not really that difficult, just unfamiliar.

Rosenlicht demonstrates how statements concerning the open subsets of a metric space can be translated into statements concerning closed subsets, or alternatively into ones concerning sequences of points and their limits. Rosenlicht closes Chapter 3 with definitions and discussions of Cauchy sequences, completeness, compactness, and connectedness.

Rosenlicht begins Chapter 4 by illustrating that the familiar epsilon-delta definition of continuity of functions can be reformulated using the metric space open ball concept, or by using open subsets in metric spaces. He further explores the interdependence of theorems about continuity, limits, and convergent sequences. Chapter 4 concludes with discussions on continuous functions on a compact metric space and on continuous sequences of functions (analogous to sequences of points).

In chapters 5 (Differentiation) and 6 (Riemann Integration) we discuss the fundamental ideas of calculus using concepts and theorems introduced in the previous chapters. At this point I revisited a favorite calculus book by Salas, Hille, and Etgen. I was pleased to find that a had a much better understanding of topics that had previously been somewhat nebulous. Rosenlicht was indeed helping me.

Nonetheless, I had substantial difficulty with the longer and more complex proofs common in the remaining 100 pages, chapters titled Interchange of Limit Operations, the Method of Successive Approximations, Partial Differentiation, and Multiple Integrals. I again visited other textbooks, but this time looking for help with topics like power series, the fixed point theorem, and the implicit function theorem. Although familiar with partial differentiation and multiple integration, I only skimmed the final chapters. I hope to return to Rosenlicht later after exploring another text on analysis.

I do recommend Introduction to Analysis, especially for students looking for a review of analysis. This Dover reprint is a good buy, even if like me, you find the later chapters to be rather difficult.

still one of the best
The book was written in 1960s, and is still one of the best. The presentation is exceptionally clear; treatment of metric spaces and elementary topology is superb. Plenty of counterexamples and good (doable) exercises (some with useful hints). The print is a bit small, but you'll get used to it. Worth every penny. More math texts should be as short, inexpensive and good as this one. Highly recommended.

a bargain
Buying this book is a no-brainer. It's only [price]. Unlike many dover books, it's not a reprint of a hundred year old text or dominated by 19th century style formal manipulations with indices running everywhere and no actual analysis or rigorous proofs. It covers the key topics of elementary real analysis (ie advanced calculus, or calculus with real proofs), which is basic to almost all fields of mathematics. In order to focus on the main ideas and definitions, it leaves out many topics and definitions (like functions of bounded variation, absolute continuity, lebesgue integration, differential forms, lebesgue covering lemma, f.i.c. etc.), so you should definitely have a more complete and comprehensive text like Apostol or Rudin (I prefer Apostol, although Rudin has complementary strengths). But for those omissions, Rosenlicht is quite a bit more readable than Apostol, which is best worked through methodically (since it contains a lot of results explicitly presented, its primary strength). Because it's both short and readable and focused, you can get through it reasonably quickly. Modern secondary school education teaches students to skip over the cursory material on elementary set theory, number systems, and strangely named but apparently obvious concepts like associativity and other field axioms, and to jump straight to the various sections with formulas in outlined boxes and procedure recipes for performing calculations. These rote recipes typically lack any conceptual unity and students are not often worse for wear forgetting or only superficially grasping previous ideas. This is a good way to never actually learn any legimate mathematics. Real math works on the principle of A->B->C->.... A proof (or your understanding of a mathematical concept) is only as strong as the weakest link in a chain. Learn and forget is not an adequate way to study math, and that's why introductory analysis is usually the course which weeds out those who will be able to explore the wider ocean of mathematical knowledge, and those for whom mathematics will be forever a giant forbidding question mark. The reality is, any above average person with the will, patience and time can learn this material and find themselves looking back thinking "Why was that so hard?" Blame it on the shabby state of secondary education. Do not skip over or gloss over the material on the real numbers if you aren't already fully conversant with the notion of l.u.b. and facile with its application (in which case why are you reading this book?). The l.u.b. property of the reals is your first real weapon to actually prove elementary theorem's of Calculus. Anyway this book isn't perfect, it's only good as an intro. and not a reference, but it serves the purpose of being accessible while still covering the key ideas and packing enough wallop to the requisite math whupping required by students numbed by years of inadequate secondary school education and the typical mechanical treatment of calculus and differential equations at the lower division level. And it's dirt cheap.

Gets right to the point with no waste of time!
In the beginning the faint of heart should beware. This book takes no time in getting to the deeper underpinnings of analysis. This makes the reader learn and become comfortable far quicker then the average book, although it can be frustrating for the first month. However, past the introduction, Rosenlicht gives an unmatched exposition of difficult material and is far more readable than most. Definately the best book in analyis for the money! Great as a stand alone text or as a supplement to a beginners course in analysis such as Russell Gordon, "Real Analysis: An Introduction." Every student should own a copy (is $8 all that much?)

An excellent introduction to real analysis
A very readable book. Any student with two years of calculus should be able to read this with understanding. Starts with metric spaces, and proceeds through differentiation, integration, interchange of limits, implicit functions. A kinder and gentler introduction, yet rigorous. ... Read more

Book Description

New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments.

The authors address the role of experimental research in the statement of new hypotheses and the discovery of new results that chart the road to future developments.

Following the lead of Mathematics by Experiment: Plausible Reasoning in the 21st Centur", this book gives numerous additional case studies of experimental mathematics in action, ranging from sequences, series, products, integrals, Fourier series, zeta functions, partitions, primes and polynomials.

Some advanced numerical techniques are also presented. ... Read more

Reviews (1)

Advanced numerical techniques, and mathematical experiments
The collaboration of Jonathan Borwein, David Bailey, and Roland Girgensohn, Experimentation In Mathematics: Computational Paths To Discovery is a scholarly, college and graduate-studies text discussing the role of computer-based experimental research in the formulation of new hypotheses. Extensive equations, advanced numerical techniques, and mathematical experiments explained in meticulous, step-by-step detail reveal the "new paradigm" in mathematic research, in this solid text especially for expert students and field professionals in cutting-edge mathematical studies. ... Read more

Reviews (5)

Excellent introduction to the philosophy of mathematics
I finished my Maths degree in 1975, so many of the more recent developments (references are made right up to 1997) were not always comprehensible to me, but I still got enjoyment out of dipping through this book.

If these 2 examples don't spark any interest for you in the discussion that followed, then this book is not for you :

Kant : The concept expressed by the English word 'triangle' contains the concept of being 'three-angled'. Does it also contain the concept of 'three-sided'? The German word for 'triangle' is 'Dreieck', or 'three-cornered'. Presumably, that concept includes 'three-angled', but, again, does it include 'three-sided'?

Formalism : Consider the equation 0=0. If you print this out, you cannot say that the equation says that the leftmost hunk of ink shaped like an oval is identical to the rightmost hunk of ink also shaped like an oval. Clearly, those are two different hunks of ink.

5 Stars for Stain on Tie!
I found this book gave an excellent and amazingly evenhanded overview of the history and contemporary state of PhiMath. Since any discussion of the Philosphy of Science usually takes only 5 minutes before getting into PhiMath, this book will also interest PhiSci-ers as well. The presentation was clear without being simplistic and without any waste. As an electrical engineer with a strong interest in PhiSci this book was the best general intro to the subject I've come across. I especially liked the large coffee stain on the author's tie on the front cover.

Incredibly clear
This is the best introduction to the philosophy of mathematics I've come across. The concepts presented are clear, up to date, and presented with a minimum of formulas and symbols. The author has an easy going style that will just pull you into this fascinating topic.

Great book for a non-philosopher
The title of my review doesn't imply that it's bad for a philosopher, but I'm mostly a student of math (so I can't speak for philosophers). Anyway, this book does seem mostly designed for people who know a bit about set theory and logic. I would also think that in any discussion of the philosophy of math, one also needs to have some understanding of mathematics as a whole (i.e. to be able to hold a semi-intelligent conversation on mathematical topics). If you have this background, then this book seems to cover (what I presume to be) the basics of the philosophy of mathematics in such a way that little background in philosophy is required. I highly recommend it.

Superb introduction to the philosophy of mathematics!
In this introductory level text Prof. Shapiro has presented a thorough introduction to the philosophy of mathematics. Not only does he discuss the three most fundamental positions in the field, but he also provides insight into more recent developments. I would highly suggest this work to anyone interested in having a solid understanding of this issues at stake in the philosophy of mathematics. Along with Paul Benacerraf and Hillary Putnam's book of philosophy of mathematics readings this is a must have! ... Read more

Book Description

Master Math: Basic Math and Pre-Algebra teaches the reader in a very user-friendly and accessible manner the principles and formulas for establishing a solid math foundation.This book covers topics such as complex fractions, mixed numbers and improper fractions; converting fractions, percents, and decimals; solving equations with logarithms or exponents, and much more. ... Read more

Reviews (5)

Good But Not Great For Basic Math and Pre-Algebra
I was sitting down at work one day and tried to work out a math problem. I couldn't believe that I had forgotten how to do certain math calculations. I am fourty years old and figured that I was in need of a mathematical review. I was able to whiz through the book and pausing after each chapter, saying to myself, "O.K. I understand this now, I haven't really lost it all. I just needed a quick refresher." The book starts out from the very very basic, explaining the theory and terminology however when it came to chapter 8 and the explanation of logarithms things start to become fuzzy. The author should have asked normal everyday students if they understood what she was talking about. I recommend Forgotten Algebra from Barron's over this book.

A big help
I have always avoided math whenever possible, but now I have to pass a college level math course in order to complete a degree. This book has helped me review the basics and slowly work my way into more advanced math.

The only reason I gave it a "4" is because I find I sometimes need to refer elsewhere for further information. That is my weakness, though. Not the books.

I would recommend this book to anyone who has to review basic math skills, and/or move on to higher math.

Great Reference Math Book
I like this book. It explains each math concept. It is a good reference tool for math.

Table of Contents
Table of Contents for the first book in the Master Math series, Basic Math and Pre-Algebra

Introduction 1

Chapter 1 Numbers and Their Operations 5

1.1. Digits and the base ten system 6 1.2. Whole numbers 7 1.3. Addition of whole numbers 7 1.4. Subtraction of whole numbers 15 1.5. Multiplication of whole numbers 22 1.6. Division of whole numbers 35 1.7. Divisibility, remainders, factors and multiples 43 1.8. Integers 45 1.9. Even and odd integers 46 1.10. Zero 47 1.11. Addition and subtraction of negative and positive integers 48 1.12. Multiplication and division of negative and positive integers 51 1.13. The real number line 52 1.14. Absolute value 53 1.15. Prime numbers 54 1.16. Rational vs. irrational numbers 54 1.17. Complex numbers 55 1.18. Rounding, truncating and estimating numbers 59 1.19. Inequalities, >, <, ¡Ý, ¡Ü 62 1.20. Factorial 66

Chapter 2 Fractions 67

2.1. Definitions 67 2.2. Multiplying fractions 68 2.3. Adding and subtracting fractions with common denominators 69 2.4. Adding and subtracting fractions with different denominators 70 2.5. Dividing fractions 76 2.6. Reducing fractions 77 2.7. Complex fractions, mixed numbers and improper fractions 78 2.8. Adding and subtracting mixed numbers 82 2.9. Comparing fractions: Which is larger or smaller? 83

Chapter 3 Decimals 87

3.1. Definitions 87 3.2. Adding and subtracting decimals 90 3.3. Multiplying decimals 93 3.4. Dividing decimals 95 3.5. Rounding decimals 97 3.6. Comparing the size of decimals 98 3.7. Decimals and money 99

Chapter 4 Percentages 101

4.1. Definitions 101 4.2. Figuring out the percents of numbers 102 4.3. Adding, subtracting, multiplying and dividing percents 105 4.4. Percent increase and decrease (percent change) 107 4.5. Simple and compound interest 109

Chapter 5 Converting Percentages, Fractions and Decimals 111

5.1. Converting fractions to percents 111 5.2. Converting percents to fractions 112 5.3. Converting fractions to decimals 113 5.4. Converting decimals to fractions 113 5.5. Converting percents to decimals 115 5.6. Converting decimals to percents 117

Chapter 6 Ratios, Proportions and Variation 118

6.1. Definitions 118 6.2. Comparing ratios to fractions and percents 120 6.3. Variation and proportion 121

Chapter 7 Powers and Exponents 123

7.1. Definition of the exponent or power 123

7.2. Negative exponents 124 7.3. Multiplying exponents with the same base 125 7.4. Multiplying exponents with different bases 126 7.5. Dividing exponents with the same base 126 7.6. Dividing exponents with different bases 128 7.7. Raising a power of a base to a power 128 7.8. Distributing exponents into parenthesis 129 7.9. Addition of exponents 130 7.10. Subtraction of exponents 131 7.11. Exponents involving fractions 131

Chapter 8 Logarithms 133

8.1. Definition of the logarithm 133 8.2. Common (base ten) and natural logarithm 135 8.3. Solving equations with logarithms or exponents 136 8.4. Exponential form and logarithmic form 138 8.5. Laws of logarithms; addition, subtraction, multiplication, division, power and radical 139 8.6. Examples: the Richter scale, pH and radiometric dating 140

Chapter 9 Roots and Radicals 145

9.1. Definitions 146 9.2. The square root 147 9.3. Estimating square roots 149 9.4. The cubed root 152 9.5. The fourth and fifth roots 153 9.6. Simplifying radicals by factoring 154 9.7. Multiplying radicals 155 9.8. Dividing radicals 155 9.9. Radicals involving fractions 156 9.10. Rationalizing the denominator 156 9.11. Addition of radicals 157 9.12. Subtraction of radicals 158

Chapter 10 Important Statistical Quantities 159

10.1. Average (arithmetic mean) 159 10.2. Median 161 10.3. Mode 163 10.4. Probability 164 10.5. Standard deviation, variance, histograms and distributions 164

Index 170

Appendix 173

Excellent Parent book to understand K-8 grade Mathematics.
I found the book in the library and took it home. I find it to be an excellent book describing every mathematical function from counting and the number line to logarithms and square roots, including fractions, decimals and percents. I'll be using this book as a reference for sequential teaching as a volunteer tutor--that's why I'm purchasing this book today. ... Read more

Book Description

When it comes to writing a text for non-music majors, Kamien knows the score. With the care you would expect from the concert pianist he is, Kamien introduces the musical elements and repertoire thoroughly and clearly, without assumptions of prior knowledge but also without condescension.As a teacher at Queens (NY) College, Kamien developed the concept of the Listening Outline, which he incorporated into the first edition of Music: An Appreciation and which he has refined and enhanced in every subsequent edition.This is a text with which students of all levels and backgrounds can feel comfortable. ... Read more

Book Description

This is a practical anthology of some of the best elementary problems in different branches of mathematics. They are selected for their aesthetic appeal as well as their instructional value, and are organized to highlight the most common problem-solving techniques encountered in undergraduate mathematics. Readers learn important principles and broad strategies for coping with the experience of solving problems, while tackling specific cases on their own. The material is classroom tested and has been found particularly helpful for students preparing for the Putnam exam. For easy reference, the problems are arranged by subject. ... Read more

Reviews (5)

Problem Solving at its best!
Finally, a book that develops problem solving techniques in a structured way for the Putnam. However, the techniques can be generally applicable to solve problems in many different areas.
The power of using "first principles" to solve problems that at first sight seem almost impossible is brought out clearly. (Example, show that any sequence of consecutive integers is divisible by n!. Where does even start to solve such problems? The book shows you how.)

You can read the book from the beginning to end, but a better way is to read it at random. Read the first chapter, though. It does a marvellous job of enumerating the different types of techniques.

Enjoy this book. You'll be amazed at how simple ideas can lead to difficult problems.

A stimulating book...
I dive inside the book. The organization by strategies is fine and ease the reading, the problems are challenging enough. If you are interessed in mathematics, student or not, buy it. You will not regret it.

How can I have not given this 5 stars yet?
I would like to suggest that the audience for this book is somewhat broader than just the "all-star" math students. I will indeed use this book to help students preparing to take the Putnam exam this fall - it is the best book I have seen for this purpose.

But in just the first two chapters, Larson presents strategies such as working backwards, modifying the problem, mathematical induction, and the pigeonhole principle, in a way which all math majors can benefit from. A graduating senior reported that once he started participating in math contests, his performance in ALL of his math classes improved. Problem solving unifies mathematical understanding. This student took the Putnam last fall (which, if you've got this far without knowing, is a six-hour national undergraduate mathematics competition taken by 3000 students in the US and Canada each year, approximately half of whom score zero) just to see what he could do, to gauge his improvement in mathematics. There isn't much more of a compliment a student could give me, intentional or otherwise.

That can't all be attributed to this book, but it is that good. The presentation is unique; the organization - by strategy, rather than by year or whatever you see in other problem books - is illuminating by itself, and has improved my pedagogy; and he just makes hard problems look easy.

Any student past the level of Linear Algebra who is up for a challenge will benefit from this book.

Excellent source for problems and problem solving techniques
This book would be especially helpful for someone planning to compete in the Putnam Exam. Lots of example covering many topics in upper undergraduate maths and of course the classic "folklore" techniques, strategies, and tools of problem solving(e.g., pigeonhole, invariants, coloring proofs, etc.). This is more of an advanced book as compared to others aimed at Olympiad contestants. Nonetheless, it is an invaluable source for anyone interested in non-routine mathematics.

Lives up to the title
An excellent resource for anyone interested in mathematical problem solving at the undergraduate level. Comes with many interesting problems taken from various mathematics contests. Additionally, the writing is clear and user-friendly. The only thing lacking is a companion workbook/solution guide. If you know anyone taking the AIME, USAMO, IMO, or Putnam exam, do them a favor and buy them this book! It's well worth it! ... Read more

Book Description

TLE is designed for learner-focused, computer classroom, lab-based, and distance learning courses. Adopting institutions receive and have license to install all TLE courses on their campus computers, even if they only adopt and have students purchase TLE for one section of one course. The pedagogical model employs a "Guided Inquiry" approach whereby students construct their own understanding of concepts. Instead of passively being fed information, students are actively involved in tasks requiring them to discover or apply mathematical concepts. Brooks/Cole Assessment, the browser-based course management system that supports TLE, allows for the easy creation of algorithmically generated, machine-graded, free-response mathematics practice, quizzes, and tests, giving instructors the power to assess student understanding of skills in a more meaningful way. Because the testing and course management system is browser-based, it can be used on a stand-alone or networked computer, or any computer with Internet access, providing instructors the ability to access course management information such as student progress, time-on-task, and grades, anytime, anywhere. Additionally, students working off campus can access TLE assignments using the Internet anytime.Adopting institutions may use Thomson Learning servers for course management at no additional cost. ... Read more

Book Description

Hailed by The New York Times Book Review as"...nothing less than a major contribution to the scientific culture of this world," this major survey features the work of 18 outstanding mathematicians. Primary subjects include analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, and theories of probability and functions. Other topics include linear and non-Euclidean geometry, topology, functional analysis, more. 1963 ed.
... Read more

Reviews (5)

Wonderful
This books is an amazing summary of almost all undergraduate math. It is definitely a mathematical masterpiece of all time, written by some of the most prominent mathematicians of all time.

Great book for math fans
I whole-heartedly agree with the other positive reviews offered here. There are only a few things I would like to add:

(1) Popular math and science has become quite popular lately. I'm sure that there are many pop-math/pop-sci readers who would like a more 'meatier' treatment of math that still has an accessible style. If you're in that group, then this book is for you.

It basically requires recollection of high school algebra and a willingness to wade through and learn some challenging material. I should add that the book looks intimidating in size but this is mostly due to the fact that Dover has bound 3 volumes as 1 (which is actually a great deal for readers).

(2) I can't think of too may books that can, with effort, take a novice through the bulk of a college/university level math curriculum.

(3) This book contains material by 2 of the greatest mathematicians/scientists of all time: Andrei Kolmogorov (famous for his work on probability and information theory as well as Kolmogorov Complexity/Algorithmic Information Theory) and I. M. Gelfand (for his work on mathematical physics). The book is worth buying for that reason alone.

Mathematics : Its Content, Methods and Meaning
It is a wonderful book. It reminds me of "The Feynman Lectures" in that it focuses on understanding, is (relatively) accessibly, has an incredible depth, and in that it covers an amazing amount. It includes "real" instruction, and you would be able to "do problems" after reading the book, although the real focus is more on understanding/ conceptual stuff.

Additional comments to my previous review
In addition to my previous review, concerning the contents, here are a few additions on physical aspects.

This 1999 paperback edition has all three volumes in one binding. The paper is thinner so the book is less bulky. Page number resets at the beginning of volume 2 and 3. (not renumbered.) Thus the book content is not altered from the 2nd edition (three volumes set) from MIT Press in 1969.

One major change is that there is one index at the end of the book which covers all three volumes. The volume is indicated together with the page number. This improves the convenience.

Excellent introduction with lots of insights
Many mathematics and engineering books today require "relatively modest background and mathematical maturity," and the text goes with mathematical formalism and compact descriptions. However, this series (three books) is a collection of chapters on single topic, written by top Russian mathematicians in plain language and vivid illustrations. Bright high school students should be able to read them, but the material is no kids stuff, in a sense that every chapter gives at least some real feeling of the topic. I recommend this series only to those who are seriously interested in mathematics but looking for the friendly version of the real mathematics. I think the title describes this.

Among the three books, I like Volume 2 the best, because Chapter 10 is on prime numbers (Mardzanisvili and Postnikov), 11 on probability theory (Kolmogorov), 12 and 13 on approximation of functions and numerical aspects, and these match with my interests the best. This volume also includes differential equations, culculus, complex analysis, etc.

Volume 1 and 3 contain analysis, topology, algebra, geometry, etc. At this paper edition price, all three are worth keeping.

A small caveat is that my review and contents description is based on the original edition by MIT press in 1960s. I assumed that second edition did not reorganize the general construction of the books. ... Read more

Book Description

Inside you'll get the practice you need to learn Algebra I, including:

Introduction

• Basic concepts
• Working with numbers

Equations and Functions

• Linear equations
• Algebraic fractions
• Polynomials and factoring
• Inequalities and absolute value inequalities
• Radicals
• Quadratic equations
• Graphing
• Systems of equations
• Functions

Problem-Solving Tools

• Clear, concise reviews of every topic
• Practice problems in every chapter–with explanations and solutions
• Complete chapter on story problems
• Diagnostic pretest to assess your current skills
• Full-length exam that adapts to your skill level

Book Description

Professor Hodges emphasizes definability and methods of construction, and introduces the reader to advanced topics such as stability.He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference. ... Read more

Reviews (1)

Excellent text, very clearly written
This is an excellent text on the model theory of first-order languages. A condensed version has also been published as: "A Shorter Model Theory."

This book is a classic. Its influence should be comparable to Keisler & Chang's famous book as *the* standard account of the relationship between the language of f.o. logic and mathematical structures. (N.B. Chang & Keisler's last edition is still useful alongside this book since the contents are not identical!)

The text is clear and fluent, as one has come to expect from this remarkable author. The book includes a detailed bibliography and suggestions for further reading. The binding and typesetting are beautifully done as well.

The short-comings are: (1) the large number of typos including an "incorrect lemma" (but with corrections available on the author's homepage), (2) the almost exclusive concentration on (untyped) first-order languages and (3) avoidance of certain speacialized topics.

All in all, this is an excellent book. ... Read more

Book Description

Processing the vast amounts of data on the Earth's land surface environment generated by NASA's and other international satellite programs is a significant challenge. Filling a gap between the theoretical, physically-based modelling and specific applications, this in-depth study presents practical quantitative algorithms for estimating various land surface variables from remotely sensed observations.
A concise review of the basic principles of optical remote sensing as well as practical algorithms for estimating land surface variables quantitatively from remotely sensed observations.
Emphasizes both the basic principles of optical remote sensing and practical algorithms for estimating land surface variables quantitatively from remotely sensed observations
Presents the current physical understanding of remote sensing as a system with a focus on radiative transfer modelling of the atmosphere, canopy, soil and snow
Gathers the state of the art quantitative algorithms for sensor calibration, atmospheric and topographic correction, estimation of a variety of biophysical and geoph ysical variables, and four-dimensional data assimilation ... Read more

Book Description

The study of complex systems in a unified framework has become recognized in recent years as a new scientific discipline, the ultimate in the interdisciplinary fields. Breaking down the barriers between physics, chemistry, and biology and the so-called soft sciences of psychology, sociology, economics and anthropology, this text explores the universal physical and mathematical principles that govern the emergence of complex systems from simple components. Dynamics of Complex Systems is the first text describing the modern unified study of complex systems. It is designed for upper-undergraduate/beginning graduate level students, and covers a broad range of applications in a broad array of disciplines. A central goal of this text is to develop models and modeling techniques that are useful when applied to all complex systems. This is done by adopting both analytic tools, including statistical mechanics and stochastic dynamics, and computer simulation techniques, such as cellular automata and Monte Carlo. In four sets of paired, self-contained chapters, Yaneer Bar-Yam discusses complex systems in the context of neural networks, protein folding, living organisms, and finally, human civilization itself. He explores fundamental questions about the structure, dynamics, evolution, development and quantitative complexity that apply to all complex systems. In the first chapter, mathematical foundations such as iterative maps and chaos, probability theory and random walks, thermodynamics, information and computation theory, fractals and scaling, are reviewed to enable the text to be read by students and researchers with a variety of backgrounds. ... Read more

Book Description

Book Description

An integral part of engineering design is the development of models that describe physical behavior or phenomena in mathematical terms.As engineering systems have become more complex, classic linear methods of modeling and analysis have proved inadequate, creating a need for nonlinear models to solve design problems. This text provides an introduction to mathematical modeling of linear and nonlinear systems, with an emphasis on the solution of nonlinear design problems.While encouraging the use of the computer as a tool for modeling and analysis, the aim is to discuss the basic concepts underlying computer techniques and to seek analytical solutions.Among topics covered are exact solution, numerical solution, graphical solution, and approximate solution methods; and the stability of nonlinear systems.Numerous examples show how to apply modeling methods to real engineering systems. The book also includes end-of-chapter problems and case studies of challenging design problems. Intended for senior or beginning graduate students, this text will also serve as a helpful reference for practicing engineers. ... Read more

Book Description

Organized, concise, convenient and usable, the latest edition ofthis nursing pharmacology textbook presents unique coverage of nursinginterventions for drug therapy with related rationales. Essential basicknowledge is presented in a logical manner, providing a balancedfoundation for current and future study and use. Special featuresinclude: a nursing process format for greater understanding andapplication of learned material; nursing actions combined withrationales help students learn the what, why and how of each situation;and attention to the particular needs of each age group; increasedemphasis on immunology; excellent discussion of the disease process;easy-to-read tables; and much, much more. A second color enhances andhighlights important aspects of the text -- students will tune in moreeasily to essential information. New in this edition: / The addition ofnew FDA-approved drugs throughout Care content in every Principlessection, including information on what to watch for at home / Heavilyrevised and reorganized chapters on: Antiarrhythmias,Antihypertensives, Pregnancy & Lactation, Antimicrobials / Expandedcontent in Chapter Two on Concepts and Process related to Drug Therapy. ... Read more

Reviews (1)

There are better choices
I am a nursing student currently using this book for pharmacology in Med-Surg I. After having worked through 7 chapters, I am not fond of this book. The authors have set it up in alomost a circular manner so that you are searching all over for the information you need. Some of the informatrion is too simple and doesn't help create a good understanding of the material. There are no pictures of cell membranes or flow charts for drug action that would help reinforce the learning that is supposed to be taking place! It's simply tedious reading that takes way too much effort to get the most out of it! ... Read more

Book Description

This book communicates the spirit of mathematics by means of simple ideas and problems, emphasizing exploration rather than drill. Its accessible approach encourages appreciation of mathematics and is ideal for readers with weak backgrounds, yet is interesting enough to involve anyone.Counting. Probability. Statistics. Geometry. Logic. Exponential Growth.Averages. Natural Numbers. Changing Bases. Clock Arithmetic. Secret Writing. Infinite Sets.Number Theory Selections.For anyone who needs to learn or review basic math concepts. ... Read more