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--- basic_tools [2017/11/29 10:40]
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-Although this is a wiki about physics, we have, of course, lots of pages about mathematics.
+<blockquote>Physics is like carpentry: Using the right tool makes the job //easier//, not more difficult. <cite> David J. Griffiths in his book "Quantum Mechanics"</cite></blockquote>
- Mathematics is the "language of nature" and physics isn't possible without it. However, in contrast to the usual Wikipedia pages about math topics, our approach can be summarized as follows: "Mathematics is a toolbox and we pick only those tools that are useful in physics".
+Although this is a travel guide to physics, you'll find here, of course, lots of pages about mathematics.
+Mathematics is the "language of nature" and physics isn't possible without it. However, in contrast to the usual Wikipedia pages about math topics, our approach can be summarized as follows: "Mathematics is a toolbox and we pick only those tools that are useful in physics".
 Especially, this means that for every mathematical concept explained here, there is a "Why is it useful?" section that explains where and how the concept is useful in physics.
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 ===== Essential Books =====
+  * [[http://www.physics.miami.edu/~nearing/mathmethods/|Mathematical Tools for Physics]] Physics by James Nearing
+  * How to Think Like a Mathematician: A Companion to Undergraduate Mathematics by Kevin Houston
   * [[https://mitpress.mit.edu/sites/default/files/titles/content/9780262514293_Creative_Commons_Edition.pdf|Street-Fighting Mathematics]] by Mahajan
   * [[https://ocw.mit.edu/resources/res-6-011-the-art-of-insight-in-science-and-engineering-mastering-complexity-fall-2014/online-textbook/MITRES_6-011F14_art_insfin.pdf|The Art of Insight in Science and Engineering by Mahajan]]
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   * No bullshit guide to math and physics by Ivan Savov
   * A Course of Mathematics for Students of Physics by Paul Bamberg and Shlomo Sternberg
+  * [[http://geometry.mrao.cam.ac.uk/2007/01/geometric-algebra-for-physicists/|Geometric Algebra for Physicists]] by Chris Doran, Anthony Lasenby
+  * [[https://link.springer.com/book/10.1007/0-306-47122-1| New Foundations for Classical Mechanics]] by David Hestenes
 ===== Essays =====
+  * [[https://betterexplained.com/articles/how-to-develop-a-mindset-for-math/|How to Develop a Mindset for Math]]
+  * [[https://betterexplained.com/articles/developing-your-intuition-for-math/|Developing Your Intuition For Math]]
+  * [[https://betterexplained.com/articles/math-cartoonist/|Learning math? Think like a cartoonist.]]
+  * [[https://betterexplained.com/articles/intuition-isnt-optional/|Learning To Learn: Intuition Isn’t Optional]],
+  * [[https://betterexplained.com/articles/learning-to-learn-embrace-analogies/|Learning To Learn: Embrace Analogies]],
+  * [[https://betterexplained.com/articles/learning-to-learn-pencil-then-ink/|Learning To Learn: Pencil, Then Ink]],
+  * [[https://betterexplained.com/articles/learning-to-learn-math-abstraction/|Learning to Learn: Math Abstraction]]
   * [[https://web.archive.org/web/20170701172117/https://www.discretization.de/media/filer_public/2014/09/05/20140413icm-proceedings-ziegler.pdf|Teaching and Learning “What is Mathematics”]] by Günter M. Ziegler and Andreas Loos
   * [[http://www.av8n.com/physics/thinking.htm|Learning, Remembering, and Thinking]] by John Denker
+  * [[https://youtu.be/XPMbCnEapQU| 13 Thinking Tools]] Robert and Michele Root-Bernstein
+  * [[https://geocalc.clas.asu.edu/pdf/Foundations.pdf| Models and Theories]] by David Hestenes
+  * [[https://geocalc.clas.asu.edu/pdf/ModelingSoftware.pdf| Modeling Software for learning and doing physics]] by David Hestenes
+  * [[http://geocalc.clas.asu.edu/GA_Primer/GA_Primer/| Primer on Geometric Algebra]]
+===== Further Recommendations =====
+  * How to Read and Do Proofs by Solow
+  * The Keys to Advanced Mathematics: Recurrent Themes in Abstract Reasoning by Solow
+  * How To Solve It by Polya
+  * Many great explanations of "pre-college" concepts can be found at https://brilliant.org/
+  * [[https://geocalc.clas.asu.edu/html/Overview.html| An Overview of Geometric Algebra in Physics]]
+===== Quotes =====
 <blockquote>Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
 <cite>[[https://www.math.fsu.edu/~wxm/Arnold.htm|V.I. Arnold]]</cite></blockquote>

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