What are the top books for various scientific topics?

[discoversci]

Hi guys,

I'm looking for a systematic list of best books for following topics:

1. Linear algebra
2. Complex analysis
3. Differential equations
4. Probability
5. Electrical circuits analysis
6. Combinatorics
7. Discrete mathematics
8. Digital signal processing
9. Quantum mechanics

3 books per topic should do (e.g. intro, intermediate, advanced). Books must be thorough. If such list already exists, please redirect me.

Much obliged !

 

[chiro]

Hey discoversci and welcome to the forums.

One thing I would like to point out is that these fields are very large fields and because they are so large, the best you can do is to focus on a particular specialty or to say that you want the best general resource (like say an introductory resource to learning).

Typically once you are up to the level where you are comfortable with the intermediate and beginning advanced stuff, you will just typically get whatever resource you can to cover a specific topic in a specific way.

Note that for mathematics texts, the way a pure mathematician will look at probability is very different to the way an applied mathematician, engineer, or even a statistician that does all applied work will treat and discuss the subject and it's important to be aware of this.

In terms of probability, there are many resources that cover the exact same thing. Many books have tonnes of problems and examples so I don't think recommending one for this case would do a lot of justice for the general introductory books.

It's going to be the same kind of thing for the rest of the topics you've mentioned, so as a preface to readers, you should pinpoint exactly what kind of speciality or focus you had in mind and if you don't have such a specific focus, you should mention that you want the best introductory books on the particular subject.

 

[discoversci]

Chiro, thanks for the comment. I totally agree and can't argue with that. There are general and more specific books in each of the listed topics. And yes, there are tons of books out there :) I'm more interested in theoretical ones ("Why" is more important for me, than "how"), but still I'd like more or less general aspect. Later I can still go further into specific topics, usually with the help of bibliography at the end of each book.
So to sum up, I'm looking for the best theoretical introductory books according to the provided list of topics.

 

[jtbell]

Many of these topics have probably been discussed in previous threads here. Have you tried the forum search feature?

 

[micromass]

1. Linear algebra

Introductory:
"Introduction to linear algebra", Serge Lang

Intermediate:
"Linear algebra", Serge Lang
"Linear algebra", Friedberg, Insel, Spence
"Linear algebra done right", Axler
"Linear algebra and its applications", Lax

Advanced:
"Linear algebra", Hoffman, Kunze
"Advanced Linear Algebra", Roman

2. Complex analysis

Introductory:
"Complex Variables", Flanigan
"Visual complex analysis", Needham

Intermediate:
"Complex Analysis", Freitag, Busam
"Complex Analysis", Serge Lang

Advanced:
"Analytic function theory", Hille

3. Differential equations

Introductory:
"Elementary Differential Equations and Boundary Value Problems" Boyce, Diprima

Intermediate:
"Differential equations: Theory, Technique and Practice", Simmons

Advanced:
"Ordinary differential equations", Arnold, Cooke

4. Probability

Introductory:
"Understanding Probability", Tijms

Advanced:
"Probability and Measure", Billingsley

6. Combinatorics
7. Discrete mathematics

Intermediate:
"Discrete and Combinatorial Mathematics", Grimaldi
"Concrete Mathematics: A foundation for computer science", Graham, Knuth, Patashnik

 

[jasonRF]

Below are a few reasonable options.

4. Probability

intro:
Ross, a first course in probability (old editions are fine - I learned from the 3rd)

intermediate:
Grimmett and Stirzaker, Probability and Random Processes (2nd edition fine. Note you can purchase complete solutions to the problems in the book as well.)

Ash, basic probability theory (More concise, but not as good or complete as Grimmett and Stirzaker. The best thing is that Dr. Ash let's you download an electronic version for free! Complete solutions also available free!)

5. Electrical circuits analysis

intermediate:
Sedra and Smith, Microelectronic Circuits (standard upper division undergrad book. Good coverage of electronics. Old editions are fine)

Desoer and Kuh, Basic Circuit Theory (intro\intermediate analysis of mostly linear circuits. In principle could be used as a first introduction, but is much better if you already know elementary circuits from a standard intro book. This is an old fashioned book from 40+ years ago. )
EDIT: I missed your second post. Given that you want theoretical intro books, perhaps this is where you should start. Note that a "theoretical" circuits book is not nearly as theoretical as, say, advanced probability theory books!

Advanced:
Gray and Meyer, Analysis and Design of Analog Integrated Circuits (standard; usually used in graduate level classes)

 

[discoversci]

micromass, jasonRF... Many thanks for your effort. I'll check these ASAP.