A guide to the intrepid adventurer
Imagine the following scenario, you are a middle age engineer that studied applied mathematics in the context of a certain field of engineering and would like to remember everything again, or better to learn everything again from the ground up! With your knowledge of having done the path once, and experience to know what is a good book, what would be the best path to revisit everything again, or to structure the best a path to a friends children or a family member life journey? This will be a journey from the most basics mathematics, all the way to pure mathematics, a real adventure along 50 books :-D
One of the most valuable resources in math from kinder garden to college math.
- Khan Academy
https://www.khanacademy.org/
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Video - The Map of Mathematics
https://www.youtube.com/watch?v=OmJ-4B-mS-Y -
The Math Book - Big Ideas Simply Explained
by DK -
The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth
by Paul Hoffman -
Logicomix: An epic search for truth
by Apostolos Doxiadis, Christos Papadimitriou
This is a series that focus on giving you a problem solving mentality, with this book series the intent is to teach you how you to solve problems with mathematics as a tool. The solution books have worked out problems, so you can rely on them for self study.
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The Art of Problem Solving: Prealgebra
by Richard Rusczyk, David Patrick, Ravi Boppana
Text: 608 pages. Solutions: 224 pages. -
The Art of Problem Solving: Introduction to Algebra, 2nd Ed
by Richard Rusczyk
Text: 656 pages. Solutions: 312 pages. -
The Art of Problem Solving: Introduction to Counting & Probability, 2nd Ed
by David Patrick
Text: 256 pages. Solutions: 120 pages. -
The Art of Problem Solving: Introduction to Geometry, 2nd Ed
by Richard Rusczyk
Text: 557 pages. Solutions: 226 pages. -
The Art of Problem Solving: Introduction to Number Theory
by Mathew Crawford
Text: 336 pages. Solutions: 144 pages.
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The Art of Problem Solving: Intermediate Algebra
by Richard Rusczyk and Mathew Crawford
Text: 720 pages. Solutions: 336 pages. -
The Art of Problem Solving: Intermediate Counting & Probability
by David Patrick
Text: 400 pages. Solutions: 208 pages.
At this point you have three good options see what adjusts better to you.
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The Art of Problem Solving: Precalculus, 2nd Ed
by Richard Rusczyk
Text: 528 pages. Solutions: 272 pages. -
Precalculus: Mathematics for Calculus 7th ed
by James Stewart, Lothar Redlin, Saleem Watson -
Precalculus
by Jay Abramson
https://openstax.org/details/books/precalculus
You will learn Linear Algebra with examples in code (Python and Matlab) without calculus.
- Linear Algebra: Theory, Intuition, Code
by Mike X Cohen
This is a book to motivate you to go further in the most beautiful way!
- Calculus Made Easy
by Silvanus P. Thompson, Martin Gardner
Then to my knowledge there are 3 similar good paths that you can follow, but with increasing depth in mathematics and Calculus.
First path
- Engineering Mathematics, 5th Ed
by Prof Anthony Croft, Dr Robert Davison, et al.
Second path
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Modern Engineering Mathematics, 6th Ed
by Glyn James, Phil Dyke -
Advanced Modern Engineering Mathematics, 5th Ed
by Glyn James, David Burley, Dick Clements, et al.
Third path
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Mathematical Methods for Physics and Engineering: A Comprehensive Guide 3rd Ed
by K. F. Riley -
Student Solution Manual 1st Ed for Mathematical Methods for Physics and Engineering 3th Ed
by K. F. Riley
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Fourier Analysis: An Introduction
by Elias M. Stein and Rami Shakarchi -
Fast Fourier Transform and Its Applications 2th Ed
by E. Brigham
Then you need to learn about Probability and Statistics the following are two nice books with a companion book with the solutions.
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Probability: For the Enthusiastic Beginner
by David J. Morin -
Introduction to Probability, Statistics, and Random Processes
by Hossein Pishro-Nik
http://www.probabilitycourse.com/preface.php -
Student's Solutions Guide for Introduction to Probability, Statistics, and Random Processes
by Hossein Pishro-Nik
http://www.probabilitycourse.com/preface.php -
All of Statistics: A Concise Course in Statistical Inference
by Larry Wasserman
Then you will need to learn about Optimization, two good books, the first with code in Julia.
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Algorithms for Optimization
by Mykel J. Kochenderfer, Tim A. Wheeler
Note: See the book PDF site link on the authors page.
https://mykel.kochenderfer.com/textbooks/ -
Convex Optimization
by Boyd, Vandenberghe
https://web.stanford.edu/~boyd/cvxbook/
- Discrete Mathematics with Applications 5th Ed
by Susanna S. Epp
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Numerical Methods for Engineers 8th Ed
by Steven Chapra, Raymond Canale -
Numerical Recipes 3rd Edition: The Art of Scientific Computing
by William H. Press -
Numerical Methods in Physics with Python
by Alex Gezerlis -
Computational Physics: Problem Solving with Python 3rd Ed
by Rubin H. Landau, Manuel J Páez, Cristian C. Bordeianu -
Applied Computational Physics
by Joseph F. Boudreau, Eric S. Swanson -
Hans Petter Langtangen - Various writings
http://hplgit.github.io/ -
Hans Petter Langtangen - Last versions
https://library.oapen.org/discover?rpp=10&etal=0&query=Langtangen%2C+Hans+Petter&scope=&group_by=none&page=1
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A Mind at Play: How Claude Shannon Invented the Information Age
by Jimmy Soni, Rob Goodman -
Information Theory, Inference and Learning Algorithms
by David J. C. MacKay
Note: In the author site you have de book and the video lectures.
http://www.inference.org.uk/mackay/itila/
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Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
by Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
Note: Book on open access.
https://www.springer.com/gp/book/9783319511023 -
Error Correction Coding: Mathematical Methods and Algorithms 2nd Ed
by Todd K. Moon
-
Schaum's 3,000 Solved Problems in Calculus
by Elliott Mendelson -
Schaum's Outline of Calculus, 6th Ed
by Frank Ayres, Elliott Mendelson -
Schaum's Outline of Advanced Calculus, 3rd Ed
by Robert Wrede, Murray Spiegel -
Schaum's Outline of Advanced Mathematics for Engineers and Scientists
by Murray Spiegel -
Schaum's Outline of Probability and Statistics, 4th Ed
by John Schiller, R. Alu Srinivasan, Murray Spiegel -
Schaum's Outline of Discrete Mathematics, 3rd Ed
by Seymour Lipschutz, Marc Lipson -
Schaum's Outline of Complex Variables, 2th Ed
by Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman -
Schaum's Outline of Differential Equations, 4th Ed
by Richard Bronson, Gabriel B. Costa -
Schaum's Outline of Partial Differential Equations
by Paul DuChateau, D. Zachmann -
Vector Analysis, 2nd Ed
by Murray Spiegel, Seymour Lipschutz, Dennis Spellman -
Schaums Outline of Tensor Calculus
by David Kay
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The Princeton Companion to Mathematics
by Timothy Gowers, June Barrow-Green, Imre Leader -
The Princeton Companion to Applied Mathematics
by Nicholas J. Higham, Mark R. Dennis, Paul Glendinning, Paul A. Martin, Fadil Santosa, Jared Tanner
This book section specific recommendation come from the wonderful video about learning pure mathematics, see the video and the video description for more details.
- Aleph 0 - How to learn pure mathematics on your own: a complete self-study guide
https://www.youtube.com/watch?v=fo-alw2q-BU
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Calculus, 4th Ed
by Michael Spivak, Michael Spivak -
Combined Answer Book For Calculus Third and Fourth Editions, 1th Ed
by Michael Spivak -
Understanding Analysis
by Stephen Abbott.
- Linear Algebra Done Right
by Sheldon Axler
And for the problems.
- Linear Algebra
by Insel, Freidberg, and Spence
- Topology through Inquiry
by Su and Starbird
- Differential Equations with Boundary Value Problems
by Zill and Cullen
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A Friendly Approach to Complex Analysis
by Sara Maad and Amol Sasane -
Visual Complex Analysis
by Tristan Needham
- Contemporary Abstract Algebra
by Gallian
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A Geometric Approach to Differential Forms
by David Bachman -
Introduction to Manifolds
by Loring Tu
- Men of Mathematics
by E.T. Bell
- The links to all my guides are in:
Guides on Linux - Programming - Embedded - Electronics - Aeronautics
https://github.com/joaocarvalhoopen/Guides_Linux-Programming-Electronics-Aeronautics
Best regards,
João Nuno Carvalho