Resources for learning how to do proofs Linear algebra

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SUMMARY

This discussion focuses on resources for learning how to construct proofs in linear algebra, particularly for those new to abstract mathematics. Key recommendations include "Principles of Mathematics" by Allendoerfer and Oakley, and "Geometry" by Harold Jacobs (not the third edition). Additionally, "Discrete Mathematics Demystified" and "Euclidean Geometry: A First Course" by Mark Solomonovich are suggested as beneficial texts. The consensus is that these resources provide a clearer understanding of proofs compared to other proof-specific books.

PREREQUISITES
  • Basic understanding of linear algebra concepts
  • Familiarity with abstract mathematical reasoning
  • Prior exposure to proof techniques
  • Knowledge of Euclidean geometry fundamentals
NEXT STEPS
  • Read the first few chapters of "Principles of Mathematics" by Allendoerfer and Oakley
  • Study the first or second edition of "Geometry" by Harold Jacobs
  • Explore "Discrete Mathematics Demystified" for foundational proof techniques
  • Examine "Euclidean Geometry: A First Course" by Mark Solomonovich for additional insights
USEFUL FOR

Students new to abstract mathematics, particularly those enrolled in linear algebra courses, and anyone seeking to improve their proof-writing skills.

caljuice
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Any resources to learn how to do proofs or view abstract math better in linear algebra?

A lot of time when I read the solution to proof questions, I don't even see how that proves the statement. The way they are written seems unintuitive. This is my first abstract math course. I've never had so much trouble in a course before. The are computations are easy though at least.
 
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linear algebra is often used as the first proofs course. It helped me however to have a prior course just on the idea of a proof in general. I learned from the first few chapters of principles of mathematics by allendoerfer and oakley. another good introduction is in the first or possibly second edition of geometry by harold jacobs, but not the third edition. other books on proofs people like are velleman, etc but i do not like many of them much myself.
 

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