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A Programmer's Introduction to Mathematics

jeremykun.com

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Re: A Programmer's Introduction to Mathematics

#211

Post by outlace »

mlejva wrote: post #139

I have a genuine question which might sound dumb but I really do wonder. How do you actually read math, physics and programming books? Reading them the same way as you'd read a novel doesn't seem right. I try to go chapter after chapter and make notes but I often get bored because I don't see the usage in my real life coding. Maybe I'm not working on problems that are challenging enough? Also after few chapters it of…

Start a software project that uses advanced math, and learn as you go in order to build the project. Learning on the job is the best way to go since you only learn the fundamentals of what’s necessary to accomplish the goal, you immediately see the utility of what you’re learning and you get a useful product at the end.

I learned substantial amounts of algebraic topology by building an open source topological data analysis library, for example.

Re: A Programmer's Introduction to Mathematics

#212

Post by Kassius509 »

monktastic1 wrote: post #38
threwythrw wrote: post #30

Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their solutions are correct. The “the reader should know if they are correct” logic doesn’t apply here. A beginner could easily have faulty logic and fool themselves into thinking their solutions are correct. I usually don’t buy math books without solutions if I’m sel…

Looks like no: "No solutions, sadly, but maybe that would be a good idea for a GitHub repo associated with the book…" https://jeremykun.com/2018/12/01/a-programmers-introduction-...

They have a repo.

https://github.com/pim-book/programmers-introduction-to-math...

Re: A Programmer's Introduction to Mathematics

#213

Post by dhodges »

Long-time programmer without a CS degree here. I've studied polynomial factoring, adding, subtracting, graphing them, etc. Sites like Khan Academy break things down in little bits but the underlying theory seldom emerges. But after working through the preview pages of this book I feel like I finally have a feel for some of the underlying theory ideas behind polynomials. This really emerged during the proofs section. The bits of code and analogies to programming really help. It was like a lightbulb going off in my brain. As a result I have ordered the book from Amazon and can't wait for it to arrive. Thank you for this book.

Re: A Programmer's Introduction to Mathematics

#214

Post by DevoidSimo »

aphextron wrote: post #199
teej wrote: post #182

Earlier quoted context omitted.

What courses did you take?

>What courses did you take? Nothing advanced, just Trig, Geometry (proofs based), Algebra and Precalculus. Basically what a sharp high school senior in college prep classes would be familiar with. Geometry was probably the best. If you've never encountered formal proofs before, it's probably the best training for pure logic I can imagine. They start out incredibly frustrating but become addictive once you figure out…

Where are you that high school only covers up to precalculus? In Australia (depending on the level) you do multivariate calculus among other things. Perhaps other subjects aren't covered as deeply.

Re: A Programmer's Introduction to Mathematics

#215

Post by andredz »

fmoralesc wrote: post #172
posterboy wrote: post #102

Earlier quoted context omitted.

What's the problem, too much empathy? I mean, if the opposite of empathy is appathy, then I don't see that in the OP.

The opposite of empathy is antipathy.

The opposite of antipathy is sympathy.

Re: A Programmer's Introduction to Mathematics

#217

Post by mindcrime »

username90 wrote: post #152
threwythrw wrote: post #146

Earlier quoted context omitted.

I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. True beginners may think they have solid intuition and a rigorous proof, but without outside validation, may have a blantant or subtle error they cannot see. The point is not to study rote solutions, but to check correctness. Edit: To your reply below, I’m talking about someone that is self-studying and h…

> I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. Yes, which is why you want a teacher until you reach that stage. > The point is not to study rote solutions, but to check correctness. Looking at others solutions can in no way prove that your solution is incorrect so I am not sure how those would help you. However having access to others solutions ofte…

It might not prove that your solution is wrong, but it can help show that your solution is correct (if you trust the provided solution), and if you made a silly mistake in your solution then seeing someone else's solution might well help you spot it.

Re: A Programmer's Introduction to Mathematics

#218

Post by mindcrime »

deadwanderer wrote: post #208
abhishekjha wrote: post #206

Earlier quoted context omitted.

>I think you aren't buying very good math books then. Just to follow up. A comment[0] on the book `Discrete Mathematics and Its Applications by Kenneth H. Rosen` `I'm convinced that math gurus are incapable of teaching math. Whenever I encounter math textbooks like this one, I'm reminded of Underpants Gnomes on South Park. For the unwashed: Underpants Gnomes stole underwear from the residents of South Park hoping tha…

May I ask what the "different text" was that you switched to? I have Rosen, and I'd like something more approachable and clear.

FWIW, I found Susanna Epp's book on Discrete Math to be more accessible than Rosen's. YMMV.

Re: A Programmer's Introduction to Mathematics

#219

Post by aphextron »

DevoidSimo wrote: post #214
aphextron wrote: post #199

Earlier quoted context omitted.

>What courses did you take? Nothing advanced, just Trig, Geometry (proofs based), Algebra and Precalculus. Basically what a sharp high school senior in college prep classes would be familiar with. Geometry was probably the best. If you've never encountered formal proofs before, it's probably the best training for pure logic I can imagine. They start out incredibly frustrating but become addictive once you figure out…

Where are you that high school only covers up to precalculus? In Australia (depending on the level) you do multivariate calculus among other things. Perhaps other subjects aren't covered as deeply.

>Where are you that high school only covers up to precalculus? In Australia (depending on the level) you do multivariate calculus among other things. Perhaps other subjects aren't covered as deeply.

I'm from the US. The state of mathematics education here is absolutely embarrassing to pretty much any other developed country. Taking precalculus is actually considered advanced, most students graduate with nothing more than an "Algebra" class that covers basic algebraic notation, quadratic equations, linear equations, and not much beyond that. Calculus 1 (single variable) is considered an advanced math class that is only taken by STEM majors for freshman university students here.

Re: A Programmer's Introduction to Mathematics

#220

Post by mindcrime »

username90 wrote: post #152
threwythrw wrote: post #146

Earlier quoted context omitted.

I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. True beginners may think they have solid intuition and a rigorous proof, but without outside validation, may have a blantant or subtle error they cannot see. The point is not to study rote solutions, but to check correctness. Edit: To your reply below, I’m talking about someone that is self-studying and h…

> I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. Yes, which is why you want a teacher until you reach that stage. > The point is not to study rote solutions, but to check correctness. Looking at others solutions can in no way prove that your solution is incorrect so I am not sure how those would help you. However having access to others solutions ofte…

Yes, which is why you want a teacher until you reach that stage.

Not everyone has that luxury.

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