Exploring Analysis: Suggested Books for High School Students

In summary, a high school student has completed their mathematical education and is now interested in Analysis. They recommend either 'Calculus' or 'Mathematical Analysis' as introductory texts, but caution against starting with a more elementary text.
  • #1
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Hi, I'm a high school student that has completed my most of my under division in mathematics (Diff. Eq., Discrete math, single/multi variable calculus, linear alg, problem solving, and basic group theory stuff) and I'm now interested in Analysis.

Can someone suggest an introductory book to this subject?
 
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  • #2
If you haven't yet learned theoretical single-variable calculus, the following three books are best to study from:

"Introduction to Calculus and Analysis Volume 1" - Richard Courant & Fritz John

"Calculus" - Michael Spivak

"Calculus" - Tom Apostol

If you have already learned this, you may want to pick up Rudin's "Principles of Mathematical Analysis", Apostol's "Mathematical Analysis" or Charles Pugh's "Real Mathematical Analysis"
 
  • #3
I read a lot of Introductory Real Analysis by A.N. Kolmogorov in middle school. Although there was quite a lot I didn't understand at a time, it was definitely a fantastic introduction. With all of your math background, I think you'll definitely be prepared for it.
 
  • #4
Either
'Calculus'
or
'Mathematical Analysis'

Both books by Binmore are modern and first rate.
 
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  • #5
Calculus and Differential Equations, as taught in high school is seldom at the same leve as the same course taught in college- and tend to vary from high school to high school or even teacher to teacher far more than college courses. That makes it difficult to say whether you should be looking at a (theoretical) calculus text or an analysis text.
 
  • #6
Introductory Real Analysis by Kolmogorov and Fomin is the most advanced of any text mentioned, so this is probably not a good place to start. There are two chapters discussing metric spaces and topological spaces, and then about 3 or 4 chapters on functional analysis, and finally three chapters on measure theory and integration. Even if you could follow many of the arguments in the text, you would still be missing out on a lot of basic real analysis, which is more elementary but fundamental. You won't get very far in Kolmogorov and Fomin if you're not well-versed in epsilon-delta arguments.

If you want a cheap intro analysis text that is fairly excellent, I would recommend Maxwell Rosenlicht's Introduction to Analysis. This text is very easy to read, and is probably a good supplement to a more comprehensive text such as Apostol's analysis text. It starts with the axioms of the real numbers and culminates with a discussion of analysis in R^n. Since you can get the Dover copy for like 10 bucks, it's also a good deal.
 

1. What is the purpose of "Exploring Analysis: Suggested Books for High School Students"?

The purpose of "Exploring Analysis: Suggested Books for High School Students" is to provide a list of recommended books for high school students who are interested in exploring the field of analysis, which is a branch of mathematics that deals with the study of limits, derivatives, integrals, and infinite series.

2. Who is the target audience for "Exploring Analysis: Suggested Books for High School Students"?

The target audience for "Exploring Analysis: Suggested Books for High School Students" is high school students who have a strong interest in mathematics and are looking to further their understanding of analysis.

3. How were the books selected for "Exploring Analysis: Suggested Books for High School Students"?

The books were selected based on their relevance to the topic of analysis and their suitability for high school students. The list was also curated by consulting with experienced mathematics educators.

4. Are these books suitable for self-study or are they meant to be used in a classroom setting?

These books can be used for both self-study and in a classroom setting. They are written in a way that is accessible to high school students, but they also provide enough depth and rigor for a thorough understanding of analysis.

5. Can these books be used as a replacement for a traditional high school mathematics curriculum?

No, these books should not be used as a replacement for a traditional high school mathematics curriculum. They are meant to supplement and enhance the understanding of analysis, but they do not cover all the topics typically taught in a high school math curriculum.

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