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A Software Engineer’s Adventures in Learning Mathematics

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Re: A Software Engineer’s Adventures in Learning Mathematics

#151

Post by bainsfather »

jeffreyrogers wrote: post #90
DennisP wrote: post #84

Earlier quoted context omitted.

I see a lot of complaints in amazon reviews about the lack of answers making self-study difficult. It got me wondering...suppose there were a website for autodidacts in math and similar topics? Something where people could post and discuss their answers to exercises. It'd solve the whole problem. Would textbook publishers sue?

I think academics would get pretty annoyed :) Most of my professors just use the exercises from the textbook for homework, usually on the assumption that you can't find the answers online.

Not a problem - Boas has the answers for every 2nd question - for tutorials, we would be asked to do the ones without answers.

Maybe DennisP's idea could do the same thing - only post answers to the odd-numbered questions. Of course, DennisP's scheme would only work for books that actually have decent end-of-section questions, unless people made up extra questions as well ...

Re: A Software Engineer’s Adventures in Learning Mathematics

#152

Post by brudgers »

j2kun wrote: post #104
brudgers wrote: post #101

I lost interest in mathematics starting in tenth grade. Looking back into the haze, it wasn't so much mathematics as high school in general and by extension industrialized education. Boredom begat indifference. Chaos reoriented priorities across starts and fits with mathematics in post-secondary education. I enrolled in Coursera's Discreet Optimization about a year ago. It was way beyond my ability [No SoA], but I le…

Discreet and discrete are two very different words :)

I already admitted it was beyond my ability...

Re: A Software Engineer’s Adventures in Learning Mathematics

#153

Post by ghufran_syed »

jordanb wrote: post #78
decasteve wrote: post #48

This topic comes up every so often. I think my previous comment applies here [1]: I started a Math degree after 16 years of programming without any Math beyond high school (the highest being high school calculus). Most of my work as a software developer didn't require any "higher" Maths. Once I began studying math, including Modern Algebra, Analysis, Graph Theory, Category Theory, etc., I realized I understood many t…

I'm in a similar boat as you. I went up through Calculus in school and hated it. Around 5 years ago I developed a strong interest in learning relevant applied math and have been enjoying it since. Some things I'd add: 1) Math is fun! If you have the aptitude and disposition to enjoy writing software you'll love working out math problems. They're little nuggets of mental stimulation that you can work on with just some…

I agree that getting things in the right order is important, but would argue that the order in which math is usually taken in the US is not the optimal one! I recently took calc-1,2,3 and linear algebra through my local community college, and then started working my way through a wonderful book on mathematical proofs:(http://www.amazon.com/Mathematical-Proofs-Transition-Advance...), as preparation for working on higher level math. I would now argue that being able to understand and write proofs is a (the?) key mathematical skill to understanding what I would call 'real' (higher) math, and could be learnt by most students following high school algebra. My impression of the calculus series and linear algebra courses was an excessive focus on calculation, the math proof book was way more fun, surprising for a subject that is often thought to be too difficult for first year college students. For those who are intimidated by the idea of a book on proofs (like I used to be), an example from the third chapter:

Theorem: Let x be an integer. Then x^2 is even if and only if x is even

It seems so simple, and I think would be accessible to anyone who had completed high school algebra but I found that even having done those calculus and linear algebra courses, I had now idea how to go about actually PROVING this! The book however, goes through the thought process step by step, and teaching the skills needed to be able to understand the real math books like Rudin.

Re: A Software Engineer’s Adventures in Learning Mathematics

#154

Post by eli_gottlieb »

seanmcdirmid wrote: post #28
eli_gottlieb wrote: post #5

Earlier quoted context omitted.

Uhhh... a rigorous Computer Science program usually stops one course short of a math minor.

Depends on your school. UW CSE (a top 10 program) would be called rigorous but is not as theoretical (there is math, but nowhere near enough for a math minor).

I went and checked the undergrad curricula back at UMass Amherst where I went. I was incorrect: a generic Comp Sci program there stops three courses short of a math minor. The more theoretical concentrations - such as Theory of Computing, Machine Learning, or Programming Languages - teach enough theoretical content to come within one course of a math/stats minor, or even cross the line.

So yes, if you take a Computer Science major with a focus on Software Engineering, you will not learn enough math to minor in math "for free". If you pick a more mathematical subfield to focus on, you should probably declare a math minor for the one or two additional courses it will take you.

I made a truly stupid choice: I graduated in 7 semesters with a Comp Sci degree concentrated on PL theory without picking up the additional courses for a math minor. As a result, I'm "condemned" to learn that material independently later on. "Luckily", the Technion required me to do extra coursework for my MSc, so I've had to buck up and learn more theory.

Now get off my lawn until I'm done with my highly theoretical machine learning exam ;-)!

Re: A Software Engineer’s Adventures in Learning Mathematics

#155

Post by anatoly »

DennisP wrote: post #84
bainsfather wrote: post #45

Earlier quoted context omitted.

It is a fantastic book. It isn't (only) a reference book though. For me it was the best way of learning the maths used in my physics degree. The book has many worked examples, and the extensive end-of-section questions have the answers in the back of the book (for every 2nd question). This means you can learn by "reading then doing", and see if you have got the answers right - something many textbooks lack. When I tr…

I see a lot of complaints in amazon reviews about the lack of answers making self-study difficult. It got me wondering...suppose there were a website for autodidacts in math and similar topics? Something where people could post and discuss their answers to exercises. It'd solve the whole problem. Would textbook publishers sue?

You can use math.stackexchange.com for this today. It's frowned upon to just ask an exercise from a book w/o even trying to solve it, but if you show that you made an effort but got stumped, or if you show your solution and ask if it's correct, people will gladly help you out.

Re: A Software Engineer’s Adventures in Learning Mathematics

#157

Post by morgante »

pjmlp wrote: post #107
coldtea wrote: post #86

Earlier quoted context omitted.

Well, I've seen software engineers with masters degrees that can't math their way out of a paper bag. In several countries. And, "validated university degress" or not, I doubt a fizz buzz interview would have much different results in your country as opposed to the US: http://blog.codinghorror.com/why-cant-programmers-program/

Most likely I would have failed fizz buzz, given that if it wasn't for HN I would have never heard of it.

> Most likely I would have failed fizz buzz, given that if it wasn't for HN I would have never heard of it.

If you required prior knowledge of Fizz Buzz to solve it successfully, you should absolutely never be hired to program anything.

Re: A Software Engineer’s Adventures in Learning Mathematics

#158

Post by bradneuberg »

Great article. I've recently been self-teaching myself machine learning the same way. I found that it started to get difficult in the middle of the course staying on track.

I decided to "scratch an itch" in open source parlance and start a study group I call colearning. Colearning provides a place for people doing remote education (or working on their own projects or writing) to have structured time to study and move forward towards their goals. It helps provide the positive pressure that a real physical class provides.

Our colearning group currently meets at Borderlands Books in San Francisco on Sunday's from 11 am to 4 pm. Message me and you can come join!

I've done this to help provide the structure I need to keep learning; its already helped me advance greatly in my own studies as I make forward progress every week.

Years ago I also identified a need for community while being self employed and started the coworking movement.

Re: A Software Engineer’s Adventures in Learning Mathematics

#159

Post by marai2 »

tel wrote: post #133

Given everyone recommending books for math autodidacts interested in learning the "breadth" of mathematics, I cannot recommend more highly Saunder's MacLane's "Mathematics, Form and Function". It reads as a high level false-historical account of how math might have been developed, in its entirety, if it unfolded in the most direct and logical way from the human experiences we all share (guided by understanding of whe…

Going back to the "breadth" recommendations, if someone wants a real appetizing sushi sampler of the breadth of Mathematics, I would highly recommend "The Joy of X" http://www.amazon.com/Joy-Guided-Tour-Math-Infinity/dp/05441... It covers a number of topics in Mathematics and makes them really easy to follow for someone with no background in Maths. I especially liked how in a few pages I succinctly understood div, grad and curl from vector calculus. For anyone wanting to start out on a full course meal of Mathematics this would make a very appetizing sampler.

Re: A Software Engineer’s Adventures in Learning Mathematics

#160

Post by decasteve »

[deleted] wrote: post #150
decasteve wrote: post #48

This topic comes up every so often. I think my previous comment applies here [1]: I started a Math degree after 16 years of programming without any Math beyond high school (the highest being high school calculus). Most of my work as a software developer didn't require any "higher" Maths. Once I began studying math, including Modern Algebra, Analysis, Graph Theory, Category Theory, etc., I realized I understood many t…

[deleted]

I had a couple of things in mind. One was means. That you can solve a problem by restating another way, in a way that it's almost indistinguishable from the original. e.g. solving a problem in linear algebra that also solves a problem in graph theory. solving a group theoretic problem that gives you an answer in topology. solving a problem using category theory that gives you a combinatorial answer, using quaternion algebra to compute a rotation, etc.

The other thing is that in Math you are often dealing with the same question but with very different objects or variable types. The same question where your numbers could be real or complex, integers or finite fields, vector spaces or topological spaces, etc., change what the "correct" answer to the question might be.

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