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Which texts have you been looking at that are too advanced for you? If you're missing some fundamental knowledge of algebra or other high school level math, yo
by wheelinsupial 4y ago
Which texts have you been looking at that are too advanced for you?
If you're missing some fundamental knowledge of algebra or other high school level math, you should refresh that. You can do so through Khan Academy (https://www.khanacademy.org/math/ https://www.khanacademy.org/math/).
The proof course I took mostly started with examples from number theory to allow students to focus on the mechanics of writing proofs. The course seems to have replaced the book I used (Mathematical Proofs: A Transition to Advanced Mathematics
Book by Albert D. Polimeni, Gary Chartrand, and Ping Zhang) with this freely accessible book https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf. This course was a prereq to the analysis, algebra, and other proof based upper level courses in math.
The most important thing is to work the examples in the chapters and solve the exercises in the back of the book. You can usually find lecture notes, problem sets, and assignment solutions on the web these days. If you're having problems with material, someone else probably has, so there is a good chance your question has been asked on Reddit or other math specific forums.
If you're more interested in math applied to computer science, then you can look for a book on discrete math. The only discrete math book I'm familiar with doesn't really make it explicit that you're learning proof techniques the way the above books do, so I can't really recommend it as a first book for self-study.
The sequence of topics covered for a course from Book of Proof by Hammack:
- Sets and basic definitions: 1.1
- Logic: 2.1, 2.2, 2.3
- Proofs: 4.1, 4.2, 4.3, 4.4, 4.5
- Logic: 2.4, 2.5, 2.6
- Contrapositive Proof: 5.1, 5.2, 5.3
- Logic: 2.7, 2.8, 2.10
- Proving non-conditional statements: 7.1, 7.2, 7.3, 7.4
- Disproof: 9.1, 9.2, 9.3
- Mathematical Induction: 10.1 and 10.3
- Sets: 1.3, 1.4, 1.5, 1.6, 1.7
- Proofs involving sets: 8.1, 8.2, 8.3
- Sets: 1.2
- Relations: 11.1, 11.2, 11.3, 11.4, 11.5
- Functions: Chapter 12
- Proof by contradiction: Chapter 6
- Cardinality: Chapter 14