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Mathematics eBooks EBooks

Free Mathematics eBooks EBooks for Download

Below we have listed all the Free Mathematics eBooks EBooks for download. Feel free to comment on any Mathematics eBooks EBooks for download or answer by the comment feature available on the page.
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Linear Methods of Applied Mathematics: This is an online textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. It is suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. Readers are expected to have completed two years of calculus and an introduction to ordinary differential equations and vector spaces. This text is suitable for students who are quite comfortable with calculus and are mainly interested in problem solving. For that reason, this text does not stress proofs, although it tries to give careful statements of theorems and to discuss the technical assumptions. Also, it does not spend much time with material like methods to calculate the integrals arising in Fourier analysis, choosing instead to appeal to software to do some calculations.

Date Added: 8/7/2008 | Visits: 31369


Basic Concepts of Mathematics: This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields, and basic properties of n-dimensional Euclidean spaces. The many exercises and optional topics (isomorphism of complete ordered fields, construction of the real numbers through Dedekind cuts, introduction to normed linear spaces, etc.) allow the instructor to adapt this book to many environments and levels of students. Extensive hypertextual cross-references and hyperlinked indexes of terms and notation add truly interactive elements to the text.

Date Added: 8/7/2008 | Visits: 30603


The Limits of Mathematics: This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. It discusses Einstein and Goedel's views on the nature of mathematics in the light of information theory, and sustains the thesis that mathematics is quasi-empirical. There is a foreword by Cris Calude of the University of Auckland, and supplementary material is available at the author's web site. The special feature of this book is that it presents a new 'hands on' didatic approach using LISP and Mathematica software. The reader will be able to derive an understanding of the close relationship between mathematics and physics. 'The Limits of Mathematics is a very personal and idiosyncratic account of Greg Chaitin's entire career in developing algorithmic information theory.

Date Added: 8/7/2008 | Visits: 32826


2 Graphs: We are concerned with graphs. Every graph contains objects that are known as nodes or vertices depending on the mood of the speaker. A graph always contains at least one node. A graph usually also contains lines that go between nodes. These lines are known as arcs or edges, again depending on the mood of the speaker.

Date Added: 8/6/2008 | Visits: 32774


9 Shortest Paths: A fundamental problem in graphs is finding the shortest path from vertex A to vertex B. Fortunately there are several simple (and efficient algorithms for doing this). We will look at the three best of these: Dijkstra’s algorithm, Floyd’s algorithm, and the Bellman-Ford algorithm. First we need to discuss different types of shortest path problems and various conventions that we will use in solving them.

Date Added: 8/6/2008 | Visits: 30535


15 Counting: Let us examine a real-life problem. As a university professor I feel that teaching twenty students for one hour a week is too much of a demand on my time and that it cuts into my research (on sour mash). Therefore, in order to cut back on my teaching load in future classes, I have decided to flunk most of my students this semester. Specifically, I am going to give one A, one B, one C, one D, and I'll flunk everyone else.

Date Added: 8/6/2008 | Visits: 32460


14 Wilson's Theorem: Wilson’s Theorem is elegant. It is not very useful, but like a lot of other people, I like it. So that is why it is here. Consider an integer n > 1. If the integer n-1! + 1 is divided by any number from 2 to n-1, it yields a remainder of 1.

Date Added: 8/6/2008 | Visits: 30332


13 Euler's Theorem and Fermat's Little Theorem: The formulas of this section are the most sophisticated number theory results in this book. The reason I am presenting them is that by use of graph theory we can understand them easily. Fermat was a great mathematician of the 17th century and Euler was a great mathematician of the 18th century.

Date Added: 8/6/2008 | Visits: 32704


12 Chinese Remainder Theorem: Many classroom exercises involve dealing cards. In this chapter we will focus on a simple problem: Write an algorithm to randomly select one card out of an ordinary 52-card deck. My students frequently derive an efficient algorithm to solve this problem. The algorithm goes as follows we use a random number generator to select a number between 1 and 52 (or between 0 and 51; either way works fine).

Date Added: 8/6/2008 | Visits: 30335


11 Division Mod n: Let's look at the values of 4x + 6y when x and y are integers. If x is -6 and y is 4 we get zero. If x is !1 and y is 1 we get 2. In fact a little experimentation will convince you that you can get all the even integers but only even integers.

Date Added: 8/6/2008 | Visits: 31489


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