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basic_tools [2017/11/29 10:39]
jakobadmin
basic_tools [2022/09/07 16:52] (current)
laserblue [Further Recommendations]
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-Although this is a wiki about physicswe have, of course, lots of pages about mathematicsMathematics is the "​language of nature"​ and physics isn't possible without itHowever, ​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. ​+<​blockquote>​Physics ​is like carpentry: Using the right tool makes the job //easier//not more difficult<​cite>​ David JGriffiths ​in his book "Quantum Mechanics"</​cite></​blockquote>​
  
-</​note>​</​WRAP>​+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 ===== ===== 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://​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]]   * [[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    * No bullshit guide to math and physics by Ivan Savov 
   * A Course of Mathematics for Students of Physics by Paul Bamberg and Shlomo Sternberg   * 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 ===== ===== 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   * [[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   * [[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]]
 +  * [[https://​youtu.be/​m7v2IUJtC3g| Professor Anthony Lasenby: A New Language for 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. <​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>​ <​cite>​[[https://​www.math.fsu.edu/​~wxm/​Arnold.htm|V.I. Arnold]]</​cite></​blockquote>​
basic_tools.1511948373.txt.gz · Last modified: 2017/12/04 08:01 (external edit)