How_to_learn_Mathematics_from_ground_up

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A guide to the intrepid adventurer

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# How to learn Mathematics from the ground up
A guide to the intrepid adventurer

## Description

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

## Important and free resource

One of the most valuable resources in math from kinder garden to college math.

* Khan Academy 
 https://www.khanacademy.org/

## Motivational books on Mathematics

1. **Video - The Map of Mathematics** 
 [https://www.youtube.com/watch?v=OmJ-4B-mS-Y](https://www.youtube.com/watch?v=OmJ-4B-mS-Y)

2. **The Math Book - Big Ideas Simply Explained** 
 by DK

3. **The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth** 
 by Paul Hoffman

4. **Logicomix: An epic search for truth** 
 by Apostolos Doxiadis, Christos Papadimitriou

## First years in math

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.

1. **The Art of Problem Solving: Prealgebra** 
 by Richard Rusczyk, David Patrick, Ravi Boppana 
 Text: 608 pages. Solutions: 224 pages.

2. **The Art of Problem Solving: Introduction to Algebra, 2nd Ed** 
 by Richard Rusczyk 
 Text: 656 pages. Solutions: 312 pages.

3. **The Art of Problem Solving: Introduction to Counting & Probability, 2nd Ed** 
 by David Patrick 
 Text: 256 pages. Solutions: 120 pages.

4. **The Art of Problem Solving: Introduction to Geometry, 2nd Ed** 
 by Richard Rusczyk 
 Text: 557 pages. Solutions: 226 pages.

5. **The Art of Problem Solving: Introduction to Number Theory** 
 by Mathew Crawford 
 Text: 336 pages. Solutions: 144 pages.

## Intermediate years in math

1. **The Art of Problem Solving: Intermediate Algebra** 
 by Richard Rusczyk and Mathew Crawford 
 Text: 720 pages. Solutions: 336 pages.

2. **The Art of Problem Solving: Intermediate Counting & Probability** 
 by David Patrick 
 Text: 400 pages. Solutions: 208 pages.

## Pre-Calculus

At this point you have three good options see what adjusts better to you.

1. **The Art of Problem Solving: Precalculus, 2nd Ed** 
 by Richard Rusczyk 
 Text: 528 pages. Solutions: 272 pages.

2. **Precalculus: Mathematics for Calculus 7th ed** 
 by James Stewart, Lothar Redlin, Saleem Watson

3. **Precalculus** 
 by Jay Abramson 
 [https://openstax.org/details/books/precalculus](https://openstax.org/details/books/precalculus)

# University or college mathematics

## Linear Algebra

You will learn Linear Algebra with examples in code (Python and Matlab) without calculus.

1. **Linear Algebra: Theory, Intuition, Code** 
 by Mike X Cohen

## Calculus and friends

This is a book to motivate you to go further in the most beautiful way!

1. **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**

2. **Engineering Mathematics, 5th Ed** 
 by Prof Anthony Croft, Dr Robert Davison, et al.

**Second path**

3. **Modern Engineering Mathematics, 6th Ed** 
 by Glyn James, Phil Dyke

4. **Advanced Modern Engineering Mathematics, 5th Ed** 
 by Glyn James, David Burley, Dick Clements, et al.

**Third path**

5. **Mathematical Methods for Physics and Engineering: A Comprehensive Guide 3rd Ed** 
 by K. F. Riley

6. **Student Solution Manual 1st Ed for Mathematical Methods for Physics and Engineering 3th Ed** 
 by K. F. Riley

## Fourier Series and Transforms

1. **Fourier Analysis: An Introduction** 
 by Elias M. Stein and Rami Shakarchi

2. **Fast Fourier Transform and Its Applications 2th Ed** 
 by E. Brigham

## Probability and Statistics

Then you need to learn about Probability and Statistics the following are two nice books with a companion book with the solutions.

1. **Probability: For the Enthusiastic Beginner** 
 by David J. Morin

2. **Introduction to Probability, Statistics, and Random Processes** 
 by Hossein Pishro-Nik 
 [http://www.probabilitycourse.com/preface.php](http://www.probabilitycourse.com/preface.php)

3. **Student's Solutions Guide for Introduction to Probability, Statistics, and Random Processes** 
 by Hossein Pishro-Nik 
 [http://www.probabilitycourse.com/preface.php](http://www.probabilitycourse.com/preface.php)

4. **All of Statistics: A Concise Course in Statistical Inference** 
 by Larry Wasserman

##  Optimization

Then you will need to learn about Optimization, two good books, the first with code in Julia.

1. **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/](https://mykel.kochenderfer.com/textbooks/)

2. **Convex Optimization** 
 by Boyd, Vandenberghe 
 [https://web.stanford.edu/~boyd/cvxbook/](https://web.stanford.edu/~boyd/cvxbook/)

## Discrete Mathematics

1. **Discrete Mathematics with Applications 5th Ed** 
 by Susanna S. Epp

## Numerical Analysis and Computational Mathematics

1. **Numerical Methods for Engineers 8th Ed** 
 by Steven Chapra, Raymond Canale

2. **Numerical Recipes 3rd Edition: The Art of Scientific Computing** 
 by William H. Press

3. **Numerical Methods in Physics with Python** 
 by Alex Gezerlis

4. **Computational Physics: Problem Solving with Python 3rd Ed** 
 by Rubin H. Landau, Manuel J Páez, Cristian C. Bordeianu

5. **Applied Computational Physics** 
 by Joseph F. Boudreau, Eric S. Swanson

6. **Hans Petter Langtangen - Various writings** 
 [http://hplgit.github.io/](http://hplgit.github.io/)

7. **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](https://library.oapen.org/discover?rpp=10&etal=0&query=Langtangen%2C+Hans+Petter&scope=&group_by=none&page=1)

## Information Theory

1. **A Mind at Play: How Claude Shannon Invented the Information Age** 
 by Jimmy Soni, Rob Goodman

2. **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/](http://www.inference.org.uk/mackay/itila/)

##  Error Correction Codes

1. **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](https://www.springer.com/gp/book/9783319511023)

2. **Error Correction Coding: Mathematical Methods and Algorithms 2nd Ed** 
 by Todd K. Moon

## Problems with answers

1. **Schaum's 3,000 Solved Problems in Calculus** 
 by Elliott Mendelson

2. **Schaum's Outline of Calculus, 6th Ed** 
 by Frank Ayres, Elliott Mendelson

3. **Schaum's Outline of Advanced Calculus, 3rd Ed** 
 by Robert Wrede, Murray Spiegel

4. **Schaum's Outline of Advanced Mathematics for Engineers and Scientists** 
 by Murray Spiegel

5. **Schaum's Outline of Probability and Statistics, 4th Ed** 
 by John Schiller, R. Alu Srinivasan, Murray Spiegel

6. **Schaum's Outline of Discrete Mathematics, 3rd Ed** 
 by Seymour Lipschutz, Marc Lipson

7. **Schaum's Outline of Complex Variables, 2th Ed** 
 by Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman

8. **Schaum's Outline of Differential Equations, 4th Ed** 
 by Richard Bronson, Gabriel B. Costa

8. **Schaum's Outline of Partial Differential Equations** 
 by Paul DuChateau, D. Zachmann

10. **Vector Analysis, 2nd Ed** 
 by Murray Spiegel, Seymour Lipschutz, Dennis Spellman

11. **Schaums Outline of Tensor Calculus** 
 by David Kay

## Very good synthesis of all around Mathematics

1. **The Princeton Companion to Mathematics** 
 by Timothy Gowers, June Barrow-Green, Imre Leader

2. **The Princeton Companion to Applied Mathematics** 
 by Nicholas J. Higham, Mark R. Dennis, Paul Glendinning, Paul A. Martin, Fadil Santosa, Jared Tanner

# To go further into Pure Mathematics

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](https://www.youtube.com/watch?v=fo-alw2q-BU)

## Real Analysis

1. **Calculus, 4th Ed** 
 by Michael Spivak, Michael Spivak

2. **Combined Answer Book For Calculus Third and Fourth Editions, 1th Ed** 
 by Michael Spivak

3. **Understanding Analysis** 
 by Stephen Abbott.

## Linear Algebra

2. **Linear Algebra Done Right** 
 by Sheldon Axler

And for the problems.

3. **Linear Algebra** 
 by Insel, Freidberg, and Spence

## Topology

1. **Topology through Inquiry** 
 by Su and Starbird

## Differential Equations

1. **Differential Equations with Boundary Value Problems** 
 by Zill and Cullen

## Complex Analysis

1. **A Friendly Approach to Complex Analysis** 
 by Sara Maad and Amol Sasane

2. **Visual Complex Analysis** 
 by Tristan Needham

## Abstract Algebra

1. **Contemporary Abstract Algebra** 
 by Gallian

## Differential Geometry

1. **A Geometric Approach to Differential Forms** 
 by David Bachman

2. **Introduction to Manifolds** 
 by Loring Tu

# The great men and women behind mathematics

1. **Men of Mathematics** 
 by E.T. Bell

# All my other guides

* The links to all my guides are in: 
 **Guides on Linux - Programming - Embedded - Electronics - Aeronautics** 
 [https://github.com/joaocarvalhoopen/Guides_Linux-Programming-Electronics-Aeronautics](https://github.com/joaocarvalhoopen/Guides_Linux-Programming-Electronics-Aeronautics)

# Have fun!

Best regards, 
João Nuno Carvalho

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