HN Books @HNBooksMonth

Hi,

I'm 30 and trying to relearn the math courses I did in college (Computer Science degree) and more. I am currently using Standford & MIT's open couseware. I feel like I am moving slower than I would if I were in a course but able to grasp the material better at this rate... I made good grades in my math courses but like you, I didn't have to use them in software engineering that much. I would like to get into a field that requires a stronger grasp of mathematics but also has a need for programming and computation (maybe machine learning or computational biology). I feel like I'm getting tired of being a software engineer (defense contractor) at a small company and looking for something higher level

Calculus (with a pdf version of the text book): https://ocw.mit.edu/resources/res-18-001-calculus-online-tex...

Linear Algebra (text book link: https://www.amazon.com/exec/obidos/ASIN/0980232716/ref=as_at...) https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...

Optimization course & book link (Stanford) https://web.stanford.edu/~boyd/cvxbook/

Statistics: http://greenteapress.com/wp/think-stats-2e/

I think this list is missing some important parts of computer science.

Here are the books that our university uses for first-year students combined with books that I found to be useful:

Introduction to Programming (using Eiffel) [1]

Mathematics for Computer Science (or: Discrete Mathematics) [2]

Introduction to Datastructures and Algorithms [3]

Introduction to Digital Design [4]

Parallel Programming (using Java) [5]

Optional but highly recommended, you'll probably find it completely out of scope:

Real Analysis I [6]

Real Analysis II [7]

Introduction to Linear Algebra [8]

Introduction to Physics [9]

[1]: http://www.amazon.com/Touch-Class-Learning-Program-Contracts...

[2]: http://ocw.mit.edu/courses/electrical-engineering-and-comput...

[3]: http://www.amazon.de/Introduction-Algorithms-Thomas-H-Cormen...

[4]: http://www.amazon.com/Digital-Design-Computer-Architecture-E...

[5]: http://www.amazon.com/Java-Concurrency-Practice-Brian-Goetz/...

[6]: http://www.amazon.com/Analysis-Texts-Readings-Mathematics-No...

[7]: http://www.amazon.com/Analysis-II-Texts-Readings-Mathematics...

[8]: http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gil...

[9]: http://www.amazon.com/Fundamentals-Physics-Extended-David-Ha...

⬐ iamryandrake

Thanks so much for this list! What's your Twitter handle I can follow you on?

Have added this list to my project!

⬐ adem

Unfortunately I don't use Twitter anymore. Good luck with your journey!

I'll take this opportunity to once again plug Strang's excellent linear algebra series [1] with associated textbook [2]. Also right now I'm working through some Cornell lecture notes [3] (that read a lot like a textbook) on manifolds and differential forms. It's meant for college sophomores and juniors who have taken linear algebra and vector calculus, though it provides a very good calculus supplement in the appendix. For me, it's perfect: the tone is informal enough to provide motivation to continue, but the definitions and proofs are fairly rigorous. It's about the only self-study math text that I think I might finish.

Hope this helps, not sure if it's over/under your level.

[1]: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...

[2]: http://www.amazon.com/exec/obidos/ASIN/0980232716/ref=nosim/...

[3]: http://www.math.cornell.edu/~sjamaar/papers/manifold.pdf

⬐ biscarch

Thanks for the suggestions.

I self-taught my way from single variable calc to somewhere around linear algebra/multivariate calc. I'm not sure how to proceed but the manifolds looks interesting.

These're good too

http://linear.ups.edu/xml/latest/fcla-xml-latest.xml#fcla-xm...

http://joshua.smcvt.edu/linearalgebra/book.pdf

Also, the common 1st year texts (Anton, Lang, Hoffman/Kunze and Friedberg/insel/Spence) can be found easily for cheap, used. The old edition of Strang I used to have was good too, but some people react really strongly when you bring it up. There's lots of ways ot sequence LA and the needs of EE's, econometrics/game theory, prob/stats and applied mathies are different from physics/math majors. Look at ToC's and read the Holyoke prof's writeup:

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gil...

(i think they're 1st year texts, my Dad's a physics prof and he started talking about determinants around 7th grade)

Subject: Linear Algebra Recommendation: Introduction to Linear Algebra by Gilbert Strang Reason: Strang presents the subject so clearly and intuitively that you feel like an expert on the subject after reading each chapter. It is by the far the best textbook I have encountered. He is also an excellent teacher and offers the lecture notes to the corresponding MIT class online.

Book: http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Edi...

Lecture: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...

⬐ harshreality

Strang is not adequate for someone looking for a rigorous presentation of linear algebra. Axler's Linear Algebra Done Right, and Halmos's (older) Finite-Dimensional Vector Spaces are superior in rigor.

⬐ cop359

Strang's hand-wavy teaching style in my opinion kinda falls apart towards the later part of the course. I feel like the whole second half is kinda half baked. I didn't come away really having a good intuitive understanding of what the SVD was or why I should care about eigenvalues. I definitely think it's a good place to start though, but if you want something a little more organized I'd really recommend.

"Matrix Analysis and Applied Linear Algebra"

http://www.amazon.com/Matrix-Analysis-Applied-Algebra-Soluti...

It's very clearly written and all the proofs are not too long nor too short. It pretty quickly goes through all the stuff Strang covers and moves on to more difficult things.

⬐ gphilip

Thank you for that recommendation; I had not heard about the book before.

An extra nice thing: the book's chapters are available for free --- for downloading and viewing, and not for other uses --- from the book's website: http://matrixanalysis.com

The course is taught by Gilbert Strang, who has written an excellent introductory textbook on the subject:

http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gil...

⬐ colanderman

Strang has another great book, Linear Algebra and its Applications: http://www.amazon.com/Linear-Algebra-Applications-Gilbert-St... Everything I know about linear algebra I learned from this book.

⬐ seanharnett

Seconded. I'm an applied math PhD student (optimization) and I use linear algebra constantly. This book taught me everything.

⬐ m0nastic

Thirded. We used an earlier edition at my school for Linear Algebra, and in spite of having a Professor who was retiring at the end of the class (complete with "I'm getting too old for this shit" demeanor), the book was approachable enough for us to get by.

⬐ cop359

A slightly more advance books which I love is: Matrix Analysis and Applied Linear Algebra by Carl Meyer. http://www.amazon.com/gp/product/0898714540

You can find a free PDF version online.

I like it more then Strang because it's a lot more concise, covers some more advanced topics and unlike Strang everything is said very accurately. I think Strang's rather hand-wavy way of explaining things starts faltering when he talks about more advance topics.

I would read Strang and listen to his lectures to get a good feel for Linear Algebra (to build up the intuition), and if you feel like you want more then pick up Meyer's book