Does math count as "technical?" I was originally a Physics major and lately I've been on a kick of filling in the mathematics that was used in my Physics classes but that I feel like was never really gone into in much depth. My current reading list is: - "Analysis I" (and II) by Terence Tao (I finished the first volume and am now on the second, but I consider them really one book) - "Understanding Analysis" by Stephe…
Riehl's "Category Theory in Context" is great. It's one of those books where every page really takes a couple hours to fully absorb. It pairs well with Milewski's "Category Theory for Programmers" [1] series, which is comparatively lighter and gives some concrete examples.
Does math count as "technical?" I was originally a Physics major and lately I've been on a kick of filling in the mathematics that was used in my Physics classes but that I feel like was never really gone into in much depth. My current reading list is: - "Analysis I" (and II) by Terence Tao (I finished the first volume and am now on the second, but I consider them really one book) - "Understanding Analysis" by Stephe…
What would you say are the prerequisites to the Analysis books? I did single-variable calculus and linear algebra in university a few years ago, but I have to admit that I'm a bit rusty.
A good intro real analysis book will have no prerequisites, really! I learned from Ross, "Elementary Analysis: The Theory of Calculus", which starts with sequences of natural numbers.
(I'm of the opinion that the usual Calc1+2+3 sequence should be scrapped in favor of everyone taking "Advanced Calculus" first. It should probably even be taught in 10th/11th grade in place of the dreadful "pre-calc" courses many schools have. Calculus didn't click for me until my first proof-based course. That's also when I learned that a "proof" is just a detailed explanation of exactly why something is true.)
Does math count as "technical?" I was originally a Physics major and lately I've been on a kick of filling in the mathematics that was used in my Physics classes but that I feel like was never really gone into in much depth. My current reading list is: - "Analysis I" (and II) by Terence Tao (I finished the first volume and am now on the second, but I consider them really one book) - "Understanding Analysis" by Stephe…
What would you say are the prerequisites to the Analysis books? I did single-variable calculus and linear algebra in university a few years ago, but I have to admit that I'm a bit rusty.
I'd definitely recommend having taken a college level Calculus course before and you'll get more out of it if you are basically comfortable with Abstract Algebra (know what sets, groups, rings, and fields are, and be able to think fairly abstractly about operations on those kinds of objects). That said, I think you could get through the first one with just high school level pre-calc although I think it would be hard to motivate yourself if you don't know enough calculus to see where it's heading. It does an absolutely brilliant job of starting with Peano's axioms to define the natural numbers, using those to define integers, using integers to define the rationals, introducing Cauchy sequences and using them to define the Reals, then introducing limits, continuity, etc. and Riemann integrals. That whole part is pretty much self contained with each concept rigorously (but clearly) built out of the previous ones. Some basic algebra and the ability to follow a mathematical argument are pretty much all you need. As it gets into the second volume, it expects some familiarity with logarithms and starts building into more advanced Calculus. It's still fairly self-contained but you might struggle if you don't remember, eg, what integration by parts looks like.
Does math count as "technical?" I was originally a Physics major and lately I've been on a kick of filling in the mathematics that was used in my Physics classes but that I feel like was never really gone into in much depth. My current reading list is: - "Analysis I" (and II) by Terence Tao (I finished the first volume and am now on the second, but I consider them really one book) - "Understanding Analysis" by Stephe…
Riehl's "Category Theory in Context" is great. It's one of those books where every page really takes a couple hours to fully absorb. It pairs well with Milewski's "Category Theory for Programmers" [1] series, which is comparatively lighter and gives some concrete examples. [1] https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
Yeah, I watched his video series on Youtube a couple years ago and really enjoyed them. Definitely a good introduction to the topic.
Does math count as "technical?" I was originally a Physics major and lately I've been on a kick of filling in the mathematics that was used in my Physics classes but that I feel like was never really gone into in much depth. My current reading list is: - "Analysis I" (and II) by Terence Tao (I finished the first volume and am now on the second, but I consider them really one book) - "Understanding Analysis" by Stephe…
Snap. I am also a physicist trying to learn math. In my case it's: - Introduction to Analysis (Mattuck) - Elementary Differential Geometry (Pressley) both chosen because they have solutions in the book, which I find important for self-study. Also just got (hot off the presses) Visual Differential Geometry and Forms (Needham) Looks fantastic! Topology is next on the list...
"A Geometric Approach to Differential Forms" by Bachman is the one that's in my Amazon shopping cart, but I'll take a look at those others as well.
I'll be reading Domain Modeling Made Functional [1], which seems fun as it applies F#/ML/FP concepts to "enterprisey" DDD. [1] https://isthisit.nz/posts/2019/domain-modeling-made-function...
My friend read that two years ago and now works for a small F# consultancy that sounds like a great place to work. He really recommends the book.
Thanks for sharing. Just curious what do people do with F# in real work nowadays? Always found it a bit peripheral comparing to Lisp, Clojure and other "main stream" functional languages.
some "out there" suggestions: - "Extremal Combinatorics" by Staysys Jukna - "Convex Optimization" by Boyd and Vandenberghe - "Delay Insensitive Circuits" [1] - "An Introduction to Mathematical Cryptography" by Hoffstein, Pipher, and Silverman - "Quantum Computing since Democritus" by Scott AAronson [1] https://www.delayinsensitive.com disclosure: I'm the author.
I'm not sure "Convex Optimization" by B&V is a good self-study book. I really struggled with it as student, and I struggled to teach with it as a TA.
It's one of those "Step 2. Draw the Rest of the Owl!" books. Great as a reference manual, but not great pedagogically. It's very complete and I would struggle to name anything better, though. Mostly, I learned convex analysis by scouring Google for lecture notes written by random professors, then cross-referencing with B&V.
My planned summer reading list: - High Performance Browser Networking by Ilya Grigorik - Refactoring: Improving the Design of Existing Code by Martin Fowler - Designing Data-Intensive Applications by Martin Kleppmann How did you find the latter? I'm a FE developer, so quite keen to get my hands on in data.
Grigorik book is awesome, must read
Can you please name its title? I'm curious about it.
I'm planning to read - Structure and Interpretation of Computer Programs (SICP). A classic. - Crafting Interpreters. Intro to compilers for me. - Deep Learning for Coders with Fastai and PyTorch. There's some other books in there too, but I'd be really happy if I finished these. I don't have a degree in CS, and most of what I know is self taught. My goal here is to fill in gaps in my knowledge as best I can.
SICP takes _ages_. I'm working through it myself but have realised it's going to be a background project for the next year or so. No idea how MIT freshman do it so quickly!
I figured that they don't have to work on most of the exercises. If you want to do that it will take forever. I'd say if I want to try it I'll just work on lab projects and just a few exercises just to warm up and stop whenever the problem is too difficult for me.