Intro to Proof Class: Velleman's How to Prove It

AI Thread Summary
Velleman's "How to Prove It" is a valuable resource for those taking an introductory proofs class. The book features a variety of exercises that range from easy to challenging, with some examples containing errors. It emphasizes the importance of using logic effectively in proofs, guiding readers on when to use direct proof, proof by exhaustion, or proof by contradiction. Although proof by induction is covered later in the book, many students may not encounter it early in their coursework. A helpful strategy for tackling difficult proofs is to translate them into symbolic logic and persist in finding a solution; seeking help after an hour of struggle is advisable. To self-check a proof, reading it critically to ensure it is convincing is recommended.
bonfire09
Messages
247
Reaction score
0
I'm taking an intro to proof's class this semester. What are your thoughts on Velleman's How to prove it book? Are the exercises easy or hard to do?
 
Physics news on Phys.org
The book has great examples (though some haves errors). The proofs can be really easy or take 30-60 minutes to do. The key point of the book is to use logic to carry out a proof the right way. It helps you decide to prove directly, by exhaustion, or by contradiction. The book goes into proof by induction much later but I haven't gone over it in class.

Tip: If you get stuck on proving a theorem, try to translate it to symbolic logic and keep trying to finish the proof. If an hour has gone by, you can go get help. This helps you try out more approaches to the problem.

Finally, one way to self check a proof is to read it and be convinced.
 

Thread '"WHAT IS A QUANTUM FIELD THEORY?" A First Introduction for Mathematicians'

The book is fascinating. If your education includes a typical math degree curriculum, with Lebesgue integration, functional analysis, etc, it teaches QFT with only a passing acquaintance of ordinary QM you would get at HS. However, I would read Lenny Susskind's book on QM first. Purchased a copy straight away, but it will not arrive until the end of December; however, Scribd has a PDF I am now studying. The first part introduces distribution theory (and other related concepts), which...
View full post »

Thread 'Books with a more theoretical approach to turbulence and DNS'

I've gone through the Standard turbulence textbooks such as Pope's Turbulent Flows and Wilcox' Turbulent modelling for CFD which mostly Covers RANS and the closure models. I want to jump more into DNS but most of the work i've been able to come across is too "practical" and not much explanation of the theory behind it. I wonder if there is a book that takes a theoretical approach to Turbulence starting from the full Navier Stokes Equations and developing from there, instead of jumping from...
View full post »

Similar threads

Foundations Looking for Introduction to Proofs
Replies
3
Views
2K
Book on how to define ideas rigorously
Replies
6
Views
2K
Introduction to Proofs texts/resources?
Replies
4
Views
4K
Introductory Analysis -- Self Studying
Replies
20
Views
3K
Courses Taking CS intro class after taking more advanced class
Replies
14
Views
1K
Suggestions for HS geometry book (proofs)
Replies
14
Views
1K
Classical Recommendation for rigorous intro books to mechanics and E&M
Replies
5
Views
3K
Calculus What Is the Best Calculus Book for Self-Learners?
Replies
17
Views
6K
Need a good real analysis book for undergrad intro course
Replies
2
Views
4K
Algebra Book on how to write proper proofs in Group Theory
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top