Home - Math 106. Visualizing a function can give a mathematician enormous insight into the function's algebraic and geometrical properties. The easiest way to see what a function looks like is to use a computer as a graphing tool. At times, this technique is the most useful, but drawing the function yourself is always the best way to get a feeling for why the function looks the way it does when graphed. All of you are by now familiar with graphing one-variable functions in the plane and hopefully can easily predict the shape of any fairly simple 2D function just by analyzing its equation. This knowledge came from graphing similar functions over and over again to get a feel for their general shape and critical points. The purpose of this tutorial is to quickly revisit these 2D examples and then to move on to drawing functions situated in 3D and even 4D space. Book of Proof. This book is an introduction to the standard methods of proving mathematical theorems.
It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews. The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. (The Cantor-Bernstein-Schröeder theorem has been added.) The two editions can be used interchangeably, except for the last few pages of Chapter 13.
Order a copy from Amazon or Barnes & Noble for $13.75 or download a pdf for free here. Part I: Fundamentals Part II: How to Prove Conditional Statements Part III: More on Proof Part IV: Relations, Functions and Cardinality Thanks to readers around the world who wrote to report mistakes and typos! Instructors: Click here for my page for VCU's MATH 300, a course based on this book. - StumbleUpon. Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields.
The lectures videos The recorded lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School. The Quicktime and MP3 formats are available for download, or you can play the Flash version directly. Each week has 3 lectures that are 50 minutes each. Review of linear algebra Groups. Permutations Cosets, Z/nZ. Quotient groups, first isomorphism theorem Abstract fields, abstract vectorspaces. Abstract linear operators and how to calculate with them Properties and construction of operators. Orthogonal groups Isometrics of plane figures Cyclic and dihedral groups. Group actions Basic properties and constructions.
A5 and the symmetries of an icosahedron Sylow theorems. Rings Examples of rings. Extensions of rings Quotient rings. MA 109 College Algebra Notes. Complex Analysis. By George Cain (c)Copyright 1999, 2001 by George Cain. All rights reserved. This is a textbook for an introductory course in complex analysis. It has been used for our undergraduate complex analysis course here at Georgia Tech and at a few other places that I know of. I owe a special debt of gratitude to Professor Matthias Beck who used the book in his class at SUNY Binghamton and found many errors and made many good suggestions for changes and additions to the book. I thank him very much. Many thanks also to Professor Serban Raianu of California State University Dominguez Hills whose many helpful suggestions have considerably improved the book.
I am also grateful to Professor Pawel Hitczenko of Drexel University, who prepared the nice supplement to Chapter 10 on applications of the Residue Theorem to real integration. The notes are available as Adobe Acrobat documents. Title page and Table of Contents Table of Contents Chapter Five - Cauchy's Theorem 5.1 Homotopy 5.2 Cauchy's Theorem.
Discrete Math Lecture Notes. Trigonometry. Abstract Algebra - Free Harvard Courses.