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Tuesday, December 27, 2011

Do you Learn Math? Need Assistance? Learning Materials? Explanations and Tools? This Post is Just for You!

If you are learning mathematics it is a matter of fact that you need good books, tools and explanations to understand and to pass the tests. As a math student by myself I am sharing with you my personal experience by category, explore them and I hope you will find all you ever needed!

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Useful Tools:
  1. Wolfram Alpha - Wolfram Alpha computational engine is a great tool to compute and solve a lot of things: integrals, equations, sums, graphs, PDE, ODE etc. All you need is to write your problem and WA will compute it to you showing you step by step solution most times.
  2. For Russian speaker students/lecturers there is the Nigma site that is almost similar to the WA site, including science information, problem solving tutorial and a lot of useful explanation.
  3. Video Lectures by MIT - Well explained, video lectures where you can understand almost every topic, here are some of them for example, others include exams, lecture notes and solutions:
  4. Video Lectures by Berkeley
  • Note: On both (1) and (2) sites you can find a lot of other info on various topics, including history, physics and other information you need.
  1. Mathematical Handbook of Formulas and Tables, 3rd (Schaum's Outline Series) by: Murray Spiegel, Seymour Lipschutz, John Liu
  1. Calculus – A Complete Course By Robert R. Adams
  2. Advanced Calculus of Several Variables By C.H. Edwards
  3. Calculus of Several Variables (Addison-Wesley series in mathematics) by: Serge Lang
  4. Calculus Late Transcendentals Single Variable 9th Ed. by: Howard Anton, Irl C. Bivens, Stephen Davis (2 parts).
  5. Student Solutions Manual Set for Calculus Early Transcendentals Single Variable 8th Edition by: Howard Anton
  6. Calculus Early Transcendentals Combined by: Howard Anton, Irl C. Bivens, Stephen Davis
Real Analysis:
Well explained, including examples and solved problems, proofs and easy reading trilogy:
  1. Real Analysis (3rd Edition) by: Halsey Royden
  2. Real and complex analysis by: Walter Rudin
  3. Real Analysis: Modern Techniques and Their Applications, 2nd Edition (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) by: Gerald B. Folland
Linear Programming/Operation Research:
If you learn or research OR you should have some useful tools in your "pocket" and I mean by this that you need Simplex Algorithm Calculator, Simplex Method Well Explained and a couple of books.
Here I will present to you some good books and tools that maybe very useful on your everyday learning or research including examples and calculator:
Operation Research Site - Easy and clear explanation of the Simplex Method - including the special cases, Operation Research Theory and step by step operations explained, friendly interface including simplex algorithm:

  1. Modeling Problems
  2. Simplex Method
  3. Two-Phase Simplex Method
  4. Graphical Method
  1. Modeling Problems
  2. Simplex Method
  3. Graphical Method
Simplex Calculator:
  1. Simplex Calculator
Some good books to study in depth the Operation Research Theory including applications:
  1. Linear Programming with MATLAB (MPS-SIAM Series on Optimization) by: Michael C. Ferris, Olvi L. Mangasarian, Stephen J. Wright
  2. Linear Programming and its Applications by: H.A. Eiselt, C.-L. Sandblom
Linear Algebra:
  1. Schaum's Outline of Theory and Problems of Linear Algebra by: Seymour Lipschutz, Marc Lipson
  2. Schaum's Outline of Matrix Operations (Schaum's Outlines) by: Richard Bronson
  3. Elementary Linear Algebra with Applications 9th edition by: Howard Anton, Chris Rorres
  4. Elementary Linear Algebra with Applications, Student Solutions Manual, 9th edition by: Howard Anton, Chris Rorres
Abstract Algebra:
Introduction to Abstract Algebra:
  1. Abstract Algebra - 3rd Edition by: David S. Dummit, Richard M. Foote
  2. Basic Abstract Algebra : For Graduate Students and Advanced Undergraduates by: Robert B. Ash
  3. Schaum's Outline of Abstract Algebra, Second Edition by: Lloyd R Jaisingh & Frank Ayres
  4. Basic Abstract Algebra by: P. B. Bhattacharya, S. K. Jain, S. R. Nagpaul
  5. Algebra: Groups, Rings, and Fields by: Louis Halle Rowen
  6. Lectures in Abstract Algebra I: Basic Concepts by: N. Jacobson
  7. Lectures in Abstract Algebra II: Linear Algebra by: N. Jacobson
  8. Lectures in Abstract Algebra III: The Theory of Fields and Galois Theory by: N. Jacobson
  9. A First Course in Abstract Algebra, Seventh Edition by: John B. Fraleigh
  10. A First Course in Abstract Algebra (Instructor’s Solutions Manual) by: John B. Fraleigh
Applications of Abstract Algebra: 
  1. Abstract Algebra with Applications (Monographs and Textbooks in Pure and Applied Mathematics) by:  Karlheinz Spindler
  2. Abstract Algebra: Theory and Applications (The Prindle, Weber & Schmidt Series in Advanced Mathematics)by: Thomas W. Judson
  3. Applications of Abstract Algebra with MAPLE by: Richard E. Klima
  1. Cryptography: Theory and Practice, Third Edition (Discrete Mathematics and Its Applications) by: Douglas R. Stinson

1 comment:

  1. Great book on artificial intelligence: http://aima.cs.berkeley.edu/ (see also http://ai-class.org and http://ml-class.org) + information theory/algorithms ML book: http://www.inference.phy.cam.ac.uk/mackay/itila/

    Fundamentals of 3D computer vision: http://www.robots.ox.ac.uk/~vgg/hzbook/

    Book on robot mapping (sorry, seems to be paid version only): http://www.springerlink.com/content/978-3-540-89883-2



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