Reddit reviews Introduction to Linear Algebra, Fifth Edition (Gilbert Strang)

I don't think there's any shortcut really... it's just a long journey you need to make. The fact you know very little now doesn't mean you're 'the stupidest person' though. At your age (whatever that is) you likely also have some human languages you've never learned before (say, Russian). The fact that you only know a few words, no grammar, and that you don't even know where to begin doesn't make you a stupid person there either. It makes you a beginner, there's a huge difference.

The tricky thing about math is that it's SO hierarchical. Every object is a dense collection of ideas that themselves sit on other ideas... but a lot of those ideas aren't /too/ bad once you find the bottom step you need to start with, you know? Check out Alcock's 'how to think about analysis' for a really great place to start. That book will start you thinking about what a proof 'is', what studying higher level math will look like, and it'll give you some regrounding in the fundamental ideas of calculus as an added bonus. Find a way to schedule review so you don't forget what you're learning.

Once you're armed to that extent at least, you'll want to get real solid with linear algebra. Strang or Boyd would be excellent choices depending on your interests (a more 'traditional' intro, vs an application heavy intro for data science).

From there, you'll want to get serious about multivariable calculus (I've heard Strang is good there too?) eventually clawing your way up to a proper statistics text (Wasserman's 'all of statistics' would be a good goal). If you're interested in bioinformatics, I don't even know what you'd be doing without a rock solid grounding in stats. You certainly couldn't read any interesting papers to stay up on what's going on, and a lot of the methods would just be crazy black box bullshit. I haven't gone into that area, but a lot of really interesting statistical techniques I've seen from a distance that have to do with what to do when you have massively more features than samples have been created by necessity to deal with problems in your specific field. If you can weather your way up through Wasserman, you'll be more than qualified to tackle Elements of Statistical Learning if you wanted to really tighten up your theoretical understanding of general ML, but a bioinformatics specific text would probably be accessible to you after Wasserman, that might make more sense ultimately. Hit what you missed in college.

The road I just laid out might look ridiculous from the side. It would probably mean setting aside at least 5 hours a week of self study for years (2~4 I imagine, depending on how quick you are at getting yourself unstuck and figuring out how to get help when needed). That might sound really intimidating, but if you intend to be in this field long term... who cares if you have a weird side hobby for a few years if it completely fills a professional hole you currently have? You don't need easy to understand youtube videos. You need an appropriate road paved with the right 10,000 exercises and such, presented with the right explanations and in the right order. The list I gave you above certainly isn't the only road or the quickest road, but it would probably work. What you really need now though is to just set aside your weekly study time and get used to the routine... you'll need to settle in for a while and make this a real part of your life if you intend to get something permanent out of it. And ideally make some friends to do it with too, this is a strangely lonely thing to do by yourself I've found, haha.

You should start with Alcock no matter what you do, but for a strange suggestion between Alcock and Strang/Boyd... check out Joshua Waitzkin's 'the art of learning'. It might have some helpful ideas for how to think about what you're going to be attempting. It's not magic, you can do this, but some ideas about what to expect and how to make the jump might help you keep your head above water during the many, many hours of work you have ahead.

Introduction to Linear Algebra by Gilbert Strang (https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-Strang/dp/0980232775/)

(Quite good when taken along with the online course: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8)

I like the format in which they are written.

> For those who prefer video lectures, Skiena generously provides his online. We also really like Tim Roughgarden’s course, available from Stanford’s MOOC platform Lagunita, or on Coursera. Whether you prefer Skiena’s or Roughgarden’s lecture style will be a matter of personal preference.
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> For practice, our preferred approach is for students to solve problems on Leetcode. These tend to be interesting problems with decent accompanying solutions and discussions. They also help you test progress against questions that are commonly used in technical interviews at the more competitive software companies. We suggest solving around 100 random leetcode problems as part of your studies.
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> Finally, we strongly recommend How to Solve It as an excellent and unique guide to general problem solving; it’s as applicable to computer science as it is to mathematics.
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> [The Algorithm Design Manual](https://teachyourselfcs.com//skiena.jpg) [How to Solve It](https://teachyourselfcs.com//polya.jpg)> I have only one method that I recommend extensively—it’s called think before you write.
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> — Richard Hamming
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> ### Mathematics for Computer Science
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> In some ways, computer science is an overgrown branch of applied mathematics. While many software engineers try—and to varying degrees succeed—at ignoring this, we encourage you to embrace it with direct study. Doing so successfully will give you an enormous competitive advantage over those who don’t.
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> The most relevant area of math for CS is broadly called “discrete mathematics”, where “discrete” is the opposite of “continuous” and is loosely a collection of interesting applied math topics outside of calculus. Given the vague definition, it’s not meaningful to try to cover the entire breadth of “discrete mathematics”. A more realistic goal is to build a working understanding of logic, combinatorics and probability, set theory, graph theory, and a little of the number theory informing cryptography. Linear algebra is an additional worthwhile area of study, given its importance in computer graphics and machine learning.
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> Our suggested starting point for discrete mathematics is the set of lecture notes by László Lovász. Professor Lovász did a good job of making the content approachable and intuitive, so this serves as a better starting point than more formal texts.
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> For a more advanced treatment, we suggest Mathematics for Computer Science, the book-length lecture notes for the MIT course of the same name. That course’s video lectures are also freely available, and are our recommended video lectures for discrete math.
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> For linear algebra, we suggest starting with the Essence of linear algebra video series, followed by Gilbert Strang’s book and video lectures.
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> > If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
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> — John von Neumann
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> ### Operating Systems
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> Operating System Concepts (the “Dinosaur book”) and Modern Operating Systems are the “classic” books on operating systems. Both have attracted criticism for their writing styles, and for being the 1000-page-long type of textbook that gets bits bolted onto it every few years to encourage purchasing of the “latest edition”.
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> Operating Systems: Three Easy Pieces is a good alternative that’s freely available online. We particularly like the structure of the book and feel that the exercises are well worth doing.
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> After OSTEP, we encourage you to explore the design decisions of specific operating systems, through “{OS name} Internals” style books such as Lion's commentary on Unix, The Design and Implementation of the FreeBSD Operating System, and Mac OS X Internals.
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> A great way to consolidate your understanding of operating systems is to read the code of a small kernel and add features. A great choice is xv6, a port of Unix V6 to ANSI C and x86 maintained for a course at MIT. OSTEP has an appendix of potential xv6 labs full of great ideas for potential projects.
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> [Operating Systems: Three Easy Pieces](https://teachyourselfcs.com//ostep.jpeg)
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> ### Computer Networking
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> Given that so much of software engineering is on web servers and clients, one of the most immediately valuable areas of computer science is computer networking. Our self-taught students who methodically study networking find that they finally understand terms, concepts and protocols they’d been surrounded by for years.
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> Our favorite book on the topic is Computer Networking: A Top-Down Approach. The small projects and exercises in the book are well worth doing, and we particularly like the “Wireshark labs”, which they have generously provided online.
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> For those who prefer video lectures, we suggest Stanford’s Introduction to Computer Networking course available on their MOOC platform Lagunita.
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> The study of networking benefits more from projects than it does from small exercises. Some possible projects are: an HTTP server, a UDP-based chat app, a mini TCP stack, a proxy or load balancer, and a distributed hash table.
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> > You can’t gaze in the crystal ball and see the future. What the Internet is going to be in the future is what society makes it.
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> — Bob Kahn
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> [Computer Networking: A Top-Down Approach](https://teachyourselfcs.com//top-down.jpg)
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> ### Databases
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> It takes more work to self-learn about database systems than it does with most other topics. It’s a relatively new (i.e. post 1970s) field of study with strong commercial incentives for ideas to stay behind closed doors. Additionally, many potentially excellent textbook authors have preferred to join or start companies instead.
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> Given the circumstances, we encourage self-learners to generally avoid textbooks and start with the Spring 2015 recording of CS 186, Joe Hellerstein’s databases course at Berkeley, and to progress to reading papers after.
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> One paper particularly worth mentioning for new students is “Architecture of a Database System”, which uniquely provides a high-level view of how relational database management systems (RDBMS) work. This will serve as a useful skeleton for further study.
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> Readings in Database Systems, better known as the databases “Red Book”, is a collection of papers compiled and edited by Peter Bailis, Joe Hellerstein and Michael Stonebreaker. For those who have progressed beyond the level of the CS 186 content, the Red Book should be your next stop.
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> If you insist on using an introductory textbook, we suggest Database Management Systems by Ramakrishnan and Gehrke. For more advanced students, Jim Gray’s classic Transaction Processing: Concepts and Techniques is worthwhile, but we don’t encourage using this as a first resource.
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