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My answer to your question is math. Learn to read and write proofs. Any intro to proofs will do: those employed in discrete math, the ones in analysis, the diag
by prostitutka 9y ago
My answer to your question is math. Learn to read and write proofs. Any intro to proofs will do: those employed in discrete math, the ones in analysis, the diagram chasing ones, whatever...Working with math proofs will definitely straighten out your thinking and whip your mind into shape.
Some suggestions to get you started:
Book of Proof by Richard Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/ https://www.people.vcu.edu/~rhammack/BookOfProof/
Discrete Math by Susanna Epp: https://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_1_5?ie=UTF8&qid=1511195716&sr=8-5&keywords=discrete+math https://www.amazon.com/Discrete-Mathematics-Applications-Sus...
Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al: https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094/ref=sr_1_1?s=books&ie=UTF8&qid=1511195770&sr=1-1&keywords=transition+chartrand https://www.amazon.com/Mathematical-Proofs-Transition-Advanc...
How to Think About Analysis by Lara Alcock: https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0198723539/ref=sr_1_9?s=books&ie=UTF8&qid=1511195842&sr=1-9&keywords=analysis https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0...
Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers: https://www.amazon.com/Learning-Reason-Introduction-Logic-Relations/dp/047137122X/ref=sr_1_1?s=books&ie=UTF8&qid=1511195907&sr=1-1&keywords=nancy+rodgers https://www.amazon.com/Learning-Reason-Introduction-Logic-Re...
Mathematics: A Discrete Introduction by Edward Scheinerman: https://www.amazon.com/Mathematics-Discrete-Introduction-Edward-Scheinerman/dp/0840049420/ref=sr_1_1?s=books&ie=UTF8&qid=1511195950&sr=1-1&keywords=scheinerman+discrete https://www.amazon.com/Mathematics-Discrete-Introduction-Edw...
The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Rafi Grinberg: https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Princeton/dp/0691172935/ref=sr_1_1?s=books&ie=UTF8&qid=1511196441&sr=1-1&keywords=analysis+lifesaver https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr...
Linear Algebra: Step by Step by Kuldeep Singh: https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/0199654441/ref=sr_1_5?s=books&ie=UTF8&qid=1511196099&sr=1-5&keywords=linear+algebra https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/...
Abstract Algebra: A Student-Friendly Approach by the Dos Reis: https://www.amazon.com/Abstract-Algebra-Student-Friendly-Laura-Reis/dp/1539436071/ref=sr_1_3?s=books&ie=UTF8&qid=1511196182&sr=1-3&keywords=abstract+algebra https://www.amazon.com/Abstract-Algebra-Student-Friendly-Lau...
That's probably plenty for a start.
- agentultra 9y agoA more graduate-level book but one I found pleasing: A Logical Approach to Discrete Mathematics: https://www.amazon.com/Logical-Approach-Discrete-Monographs-Computer/dp/0387941150 https://www.amazon.com/Logical-Approach-Discrete-Monographs-... And a more pragmatic approach to the same material (with a lot of cross-over in terms of proof-style, etc): Programming in the 1990s: http://www.springer.com/gp/book/9780387973821 http://www.springer.com/gp/book/9780387973821 But one I particularly enjoyed early on was written for liberal-arts level students of maths (who might've been traumatized by maths in the past): Introduction to Graph Theory: https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709/ref=pd_sim_14_1?_encoding=UTF8&psc=1&refRID=033XBN1NVFEAHARTB6M2 https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathe... It will actually get you into writing proofs in set theory within the first couple of chapters.
- bordercases 9y agoOh gosh the equational logic rabbit hole. To add to the fire: http://mathmeth.com/ http://mathmeth.com/
- mezod 9y agogreat, thank you!