Book Recommendations for Proofs

Click For Summary
SUMMARY

The discussion centers on recommendations for books that introduce undergraduate and graduate mathematics, emphasizing the importance of exercises and clear explanations. "Elementary Number Theory" by David M. Burton is highlighted as an excellent starting point for those transitioning from high school math, as it covers various proof techniques and includes numerous exercises. The conversation also notes that undergraduate and graduate mathematics encompasses distinct subjects such as analytical geometry, linear algebra, abstract algebra, calculus, and discrete mathematics, which are essential for understanding proofs.

PREREQUISITES
  • Familiarity with high school mathematics concepts
  • Understanding of basic proof techniques
  • Knowledge of undergraduate mathematics subjects such as linear algebra and abstract algebra
  • Ability to engage with mathematical exercises and problem-solving
NEXT STEPS
  • Explore "Elementary Number Theory" by David M. Burton for foundational proof techniques
  • Research additional resources on analytical geometry and its applications
  • Investigate linear algebra textbooks that focus on proof-based learning
  • Review MathOverflow discussions for curated lists of books on mathematical proofs
USEFUL FOR

Students transitioning from high school to college-level mathematics, educators seeking effective teaching resources, and anyone interested in developing a strong foundation in mathematical proofs and techniques.

kanderson
I want a good book with an introduction to either graduate or undergraduate mathematics that has excercises and clear explanations.
 
Physics news on Phys.org
kanderson said:
I want a good book with an introduction to either graduate or undergraduate mathematics that has excercises and clear explanations.
I have never seen any book titled "Intro to undergrad math". Maybe there are such books but I don't know.
"Elementary Number Theory by David M Burton" is an excellent book. If one wants to start reading non High School math then I guess this is a good place to start. You will get to know numerous proof techniques not used at all in high school. It has a lot of exercises too.
 
Undergraduate, and especially graduate, math is divided into subjects: analytical geometry, linear algebra, abstract algebra, calculus, discrete mathematics and so on. I personally never studied any generic higher math or proof methods per se; I studied the subjects above and in the process I learned how proofs work.

That said, when I started college I already had a good background in math, so starting abstract algebra directly may not work for everyone. This thread on MathOverflow seems to have a nice selection of books about proofs.
 

Similar threads

Other Recommendation for Mathematics for Physicist and Engineers book
  • · Replies 6 ·
Replies
6
Views
3K
MHB Combinatorics book recommendation.
  • · Replies 2 ·
Replies
2
Views
2K
Intro Math Hassani's books on Mathematical Physics/Methods
  • · Replies 5 ·
Replies
5
Views
5K
Book recommendation after Sakurai Modern Quantum Physics
  • · Replies 3 ·
Replies
3
Views
897
Suggestions for HS geometry book (proofs)
  • · Replies 14 ·
Replies
14
Views
3K
Books on Weak Interaction
  • · Replies 0 ·
Replies
0
Views
1K
Recommendations for study materials to prepare for undergrad Physics
  • · Replies 7 ·
Replies
7
Views
3K
Book recommendations (abstract algebra and number theory)
  • · Replies 5 ·
Replies
5
Views
4K
Any book recommendations for strengthening my understanding of the basics of mechanics?
  • · Replies 16 ·
Replies
16
Views
4K
Intro Physics Book Recommendations For a 13 Year Old
  • · Replies 21 ·
Replies
21
Views
5K