Need recommendation on Advanced Calculus books

[tolgaist]

Recommendation needed

Hi ,

I am taking mathematics course in fe class. But i don't have a mathematical background!

Is there any "basic" book that I can understand which include examples?

your urgent help is needed. Tx in advance.

"Random variables, Probability theory, expectations and variance, Binomial, Poisson and Normal Distributions, Law of Large Numbers; methods of data analysis, univariate and multi-variate models, estimation, confidence intervals, hypothesis testing problems, analysis of variance, regression and correlation analysis, goodness of fit tests, maximum likelihood estimation; Central Limit Theorems, generating and characteristic functions, moments, conditional probabilities; Markov Chains, random walks as martingales, discrete to continuous stochastic processes, binomial model of stock prices, Arbitrage Pricing Theory, pricing of a European Call Option, Black-Scholes equation."

 

[Andy Nguyen]

This sounds like a call for the Math Primer by Stefanica. It's a calculus-based approach with financial engineering applications.

Dan Stefanica's A Primer for the Mathematics of Financial Engineering

 

[CGiuliano]

"Random variables, Probability theory, expectations and variance, Binomial, Poisson and Normal Distributions, Law of Large Numbers; methods of data analysis, univariate and multi-variate models, estimation, confidence intervals, hypothesis testing problems, analysis of variance, regression and correlation analysis, goodness of fit tests, maximum likelihood estimation; Central Limit Theorems, generating and characteristic functions, moments, conditional probabilities; Markov Chains, random walks as martingales, discrete to continuous stochastic processes, binomial model of stock prices, Arbitrage Pricing Theory, pricing of a European Call Option, Black-Scholes equation."

This may also be helpful to supplement your text:

Amazon.com: Schaum's Outline of Probability, Random Variables, and Random Processes (9780070306448): Hwei Hsu: Books

 

[chaoticrambler]

Elementary real analysis by Rudin (or Baby Rudin) is still the Gold Standard. It will go well with your required textbook.

 

[Dave Haan]

Glad to hear baby Rudin is still so well regarded (my 1st time thru was 30 yrs ago, the last time, 10 yrs). I also found the follow-ons, Rudin's Real & Complex Analysis, and Functional Analysis, as clear and as relevant to financial analysis.

 

[Tyler Tuan]

Yes! Baby rudin. Had it last year.

 

[MRoss]

Usually the professor offering the course has the best idea. Why not ask him/her?

 

[Curiousasd]

Since my original post I've completed the first semester in Advanced Calculus. I've looked through at least a dozen of books, and the winner is...

Introduction to Real Analysis by Bartle and Sherbert. It skips some minor explanations but it is the most comprehensive textbook on the subject. I wish it had more hints or answers to problems to make it even more suitable for self-study. The notation seems outdated. It is not cheap even used but it is nice to own it.

The other two books I liked and used:
Analysis: With an Introduction to Proof by Steven Lay. This one has less material but more explanations.

A First Course in Mathematical Analysis, by Burkill. It is very basic but the explanations are excellent.

IMHO, the combination of these three books is the best "real line" treatment on analysis.

The textbook required for my class:
Advanced Calculus by Patrick M. Fitzpatrick. It is terrible. You cannot possibly learn from it, expecially without help.

Thanks everyone, esp. bbw for help!!

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Hey there

I am really wanting to know why everyone recommends Bartle for introductory real analysis. Apparently it really is too scanty on examples, explanations and, most regrettably, on proofs. A few have pointed out that it's no good due to the severe omissions in proofs.

I have a collection of 10 real analysis books now with 4 advanced calculus titles too. Am collecting the best ones for novices. Do you think 10 is too overboard? I am a passionate collector of outstanding calculus texts.

What has been your experiences with bartle & sherbert specifically. I guess it may be Ok for those cool with proof steps omissions and not so for others wanting a deep detailed exposition?

I mean I have Petrovich Advanced Calculus and a whole lot of others. From discussions here and online I am tempted to add on even more into my collection such as Bryant, Schramm etc.

What advice would you guys give?