Really want to study formal math with proofs

In summary, the conversation revolves around the topic of finding good books for studying formal math with proofs. The participants recommend various books, such as Calculus Concepts and Contexts by James Stewart and Apostol's One-Variable Calculus, for introductory calculus with proofs. They also mention the importance of practicing problems and understanding concepts thoroughly. Additionally, they discuss resources for learning proofs, such as Solow's How to Read and do Proofs and Schaum's Outlines. The conversation ends with a question about the better option between Rea Problem Solver for Calculus and Schuman Outline to Calculus.
  • #1
Weave
143
0
I was wondering i really want to study formal math with proofs etc. Are there any good books out there?
 
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  • #2
What level?

- Warren
 
  • #3
Well, knowing what sub-discipline of math you're interested in would help ( I wouldn't be able to answer anyway, but I am sure that info will be needed :P)

Try the science book reviews at the top of this forum (Academic Advice.) There should be some good stuff there, I will look for a good thread for you as I think I remember one.
 
  • #5
I can personally recommend Calculus Concepts and Contexts by James Stewart for introductory calc. Although I think Apostle is better for proof based Calculus.
 
  • #6
Yah I really like Math.. I am not just sure where to start. I really want to get down to the roots. Keep in mind I will be starting Calc next Semester.
 
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  • #7
Well I think I would be able to help you there. How comfortable are you with algebra? Do you know all your exponent laws real good? Binomial theorem, trigonometry, stuff like that.
 
  • #8
Any good calc book (Apostol is the best, IMO) will have many, many proofs you can mull over.

- Warren
 
  • #9
Oh man yah I defiantely got Algebra down, but still enjoy it. Trig, Binomial, yup know them too. Easy stuff.
 
  • #10
Try Apostol then, maybe Chroot knows the title of the textbook but I have a feeling its something like One-Variable Calculus with an introduction to Linear Algebra.

I liked James Stewart since it was more applied then Apostol, was geared more so to scientists/engineers than mathematicians. But if you like the proofs/rigorous type stuff, I think Apostol is the way to go.
 
  • #11
chroot said:
Any good calc book (Apostol is the best, IMO) will have many, many proofs you can mull over.

- Warren

Does Apostol have proofs, or does he just ask you to write them?

For example, Spivak asks you to write many many proofs, yet lacks the ability to have some of this one. The ratio of examples to exersices is like 1:50.
 
  • #12
I can pull out my copy and check the 'ratio,' but I believe it has more proofs than do many other texts.

- Warren
 
  • #13
Yah I really want to build up a good library of knowledge of math not just for school, but just for pure satisfaction. I would like to in the long run look at tensors, etc.-I will probably end up studing math most my life for leisure.
 
  • #14
The Schaum's outlines might be right up your alley, too, if you intend to do a lot of self-teaching. They're cheap and have hundreds of worked examples. They don't have many proofs, but they might complement a thorough textbook nicely for you.

- Warren
 
  • #15
Cool, what about advanced Geometies like: Non-Euclid Geometries/hyper geometries and proofs of those?
 
  • #16
For Calculus use Louis Leithold's TC 7
 
  • #17
Any advice on mastering Calc 1-3?
Just work tons of examples?
 
  • #18
Do tons of problems and try to understand everything. I found that if I skipped over something that didn't make sense than later down the road I would find myself not knowing to how to solve stuff. As you probably know, you can't read a math text like a social text, can't skip stuff, it all builds on each preceding topic.

Do every single problem in the book if you want to master it, its the only way.
 
  • #19
I would also look at a book on proofs. (I used Solow's How to Read and do proofs.) I was only familiar with two column proofs that I did in geometry, so I needed a little help writing proofs. You might not need that though. :)
 
  • #20
Which one is better: Rea Problem Solver for Calculus? Or Schuman Outline to Calculus?
 

Related to Really want to study formal math with proofs

1. What is formal math with proofs?

Formal math with proofs is a branch of mathematics that focuses on using logical reasoning and rigorous demonstration to prove the truth of mathematical statements. It involves breaking down complex concepts into smaller, more manageable steps and providing evidence for each step in order to arrive at a verifiable conclusion. This approach allows for a deeper understanding of mathematical concepts and their applications.

2. Why should I study formal math with proofs?

Studying formal math with proofs can help you develop critical thinking and problem-solving skills, as well as improve your overall mathematical ability. It also provides a strong foundation for further studies in mathematics and related fields such as computer science and engineering. Additionally, many fields, such as finance and data analysis, require a strong understanding of formal math with proofs for making accurate and informed decisions.

3. What are some common topics covered in formal math with proofs?

Some common topics covered in formal math with proofs include logic and set theory, algebra, calculus, number theory, and geometry. These topics are often explored in depth, with a focus on understanding the underlying principles and proof techniques. As you progress in your studies, you may also encounter more advanced topics such as topology, abstract algebra, and real analysis.

4. Is formal math with proofs difficult to learn?

Formal math with proofs can be challenging, but it is a highly rewarding and valuable subject to study. It requires a strong foundation in basic mathematical concepts, as well as patience and persistence in working through complex problems. With practice and dedication, anyone can learn formal math with proofs and develop the necessary skills to excel in this field.

5. What are some resources for learning formal math with proofs?

There are many resources available for learning formal math with proofs, including textbooks, online courses, and instructional videos. Your school or university may also offer courses or workshops on this subject. It can also be helpful to join a study group or work with a tutor to receive personalized guidance and support. Additionally, practicing regularly and actively engaging with the material are key to mastering formal math with proofs.

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