Book Recommendations for Proofs

In summary, the conversation is about finding a good book with an introduction to either graduate or undergraduate mathematics that includes exercises and clear explanations. The person mentions not knowing of any books specifically titled "Intro to undergrad math" but suggests "Elementary Number Theory by David M Burton" as a good starting point for non-high school math. They also mention that undergraduate and graduate math is divided into different subjects and that they personally didn't study generic higher math or proof methods, but rather learned through studying specific subjects. They suggest checking out a thread on MathOverflow for recommendations on books about proofs.
  • #1
kanderson
I want a good book with an introduction to either graduate or undergraduate mathematics that has excercises and clear explanations.
 
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  • #2
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.
 
  • #3
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.
 

Related to Book Recommendations for Proofs

1. What is a "Book Recommendation for Proofs"?

A "Book Recommendation for Proofs" is a book or resource that provides guidance and instruction on how to construct and write mathematical proofs. These books typically cover topics such as logic, reasoning, and proof techniques specific to various mathematical fields.

2. Why is it important to have a good book recommendation for proofs?

A good book recommendation for proofs is important because learning how to construct and write mathematical proofs is a fundamental skill in many areas of scientific research. Having a reliable resource can help improve understanding and efficiency in this process.

3. How do I choose the right book recommendation for proofs?

Choosing the right book recommendation for proofs depends on various factors, such as your level of proficiency and the specific mathematical field you are studying. It is essential to research and read reviews to find a book that aligns with your learning style and goals.

4. Are there any free resources for book recommendations for proofs?

Yes, there are many free resources available for book recommendations for proofs. Online forums and discussions among mathematicians and students can provide valuable insights and recommendations. Additionally, many universities and libraries offer free access to e-books and other resources.

5. Can I rely solely on a book recommendation for proofs to improve my skills?

No, while a book recommendation for proofs can be a helpful guide, it is essential to practice and apply the concepts learned in the book. Seeking guidance from a mentor or participating in study groups can also enhance your skills in constructing and writing mathematical proofs.

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