Linear Algebra / Vector Calc Text (for CompSci student)

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Discussion Overview

The discussion revolves around recommendations for textbooks in Linear Algebra and Vector Calculus suitable for a Computer Science undergraduate student. The participant expresses a need for accessible resources due to a compressed course structure and challenges with proofs and mathematical maturity.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant mentions their struggle with proofs and seeks recommendations for textbooks that are more approachable, specifically mentioning "Linear Algebra: A First Course in Pure and Applied Math" by Edgar G. Goodaire.
  • Another participant suggests that "Linear Algebra Done Right" may be challenging without prior experience with proofs and recommends "Linear Algebra and Its Applications" by Lay as a more application-oriented alternative.
  • A different participant agrees that "DIV, Grad, Curl, & All That" by Schey is good for applications in electrodynamics but may not be suitable for a first experience in vector calculus, suggesting that the participant consider the calculus textbook they used for potential content on multivariable calculus.
  • One participant mentions that "Mathematical Methods For Engineers And Scientists" was helpful for them in similar courses and notes that they borrowed a book titled "Calculus: Single and Multivariable" that covers their syllabus for vector calculus, despite poor reviews.
  • A final contribution provides a link to a free linear algebra book, suggesting an alternative resource for the participant.

Areas of Agreement / Disagreement

Participants express differing opinions on the suitability of specific textbooks, indicating that there is no consensus on the best resources for the participant's needs. Multiple competing views on the recommended texts remain unresolved.

Contextual Notes

Some participants highlight the importance of prior experience with proofs when selecting textbooks, indicating that the participant's mathematical maturity may affect their ability to engage with certain texts. There are also references to specific course structures and personal experiences that may not apply universally.

Adyssa
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I'm taking a Linear Algebra / Vector Calculus course this semester as part of a maths major for my Comp Sci undergrad. degree. We don't have a prescribed text, but I'd very much like a hard copy of something that I can reference. The course is somewhat compressed compared to what the Maths degree students take, and my experience with these courses so far is that I'm learning stuff, quickly, but not deeply. I smashed a compressed Calc (not sure if we made it to Calc II, we did an awful lot of integration techniques on top of regular differentiation and integration) in a single course last semester and I hung on for dear life and ended up with half decent marks. I took Numerical Methods at the same time and it almost killed me! I don't have much in the way of mathematical maturity and found some of the quadrature techniques, and the like, to be way over my head in terms of the proofs, although I could use them in practise to some extent. We made it to Runge-Kutta and touched on ODEs and I really struggled at that point.

I've found a few threads in the Linear Algebra forum, and have been looking at these books that were mentioned on Amazon:


Linear Algebra by G. E. Shilov


Linear Algebra Done Right by Sheldon Jay Axler

Which seem like solid texts. It seems I'm going to be seeing a lot of proofs, and my past experience with proofs is really bad, I have a lot of trouble with them. The last one that really messed with me was the Pumping Lemma, which I just couldn't apply properly to the range of problems we were provided. I just don't seem to think in the correct fashion for proofs. With that in mind, I came across this text:

Linear Algebra: A First Course in Pure and Applied Math by Edgar G. Goodaire

Which seems to focus on learning how to read proofs, sounds great, but I can't find a review on the text itself.

As for Vector Calc, this text has very good reviews:

DIV, Grad, Curl, & All That: An Informal Text on Vector Calculus by Harry M. Schey

I wonder if anyone has advice and/or other text recommendations for me? :)
 
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Linear Algebra Done Right might be difficult if you haven't had previous experience with proofs. I recommend a more applications/computational orientated book like Lay's Linear Algebra and Its Applications.

The book you posted under vector calculus is good if you want to understand how to apply vector calculus to electrodynamics, but not for a first experience. Which book did you use for calculus? It might have chapters on multivariable and vector calculus.
 
Schey is a great book but it is not a vector calculus textbook. Marsden is a full vector calc book and I have enjoyed it a lot.

Shilov is too advanced I imagine. This is a lower division course yeah? Lay or anton are good LA books.
 
I didn't have a prescribed textbook for calc and vectors/matrices, we relied on printed notes, but I have a copy of "Mathematical Methods For Engineers And Scientists" which is written by two profs at my uni (can't find it on Amazon) that served me pretty well when I got stuck.

Also, I just borrowed this book from a friend, and it seems to cover my syllabus wrt vector calculus, although the reviews at Amazon are poor.

Calculus: Single and Multivariable

The Lay and Anton LA books both look good, thanks for the recommendations there, I'm reading up on Marsden and some other vector calc texts. :)
 

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