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Ask HN: Math books like SICP?

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Re: Ask HN: Math books like SICP?

#41

Post by alok-g »

oskarth wrote: post #38

Not the same type of book, but you could do a lot worse than reading through Mathematics: Its Content, Methods and Meaning , by M. A. Lavrent’ev, A. D. Aleksandrov, A. N. Kolmogorov. It's an amazing book which gives a mathematical (but not rigorous in the sense of proofs etc.) overview of most of mathematics. http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

+1.

The best thing I like about this book is that it often first gives a real-life example of a problem, then gives some history of how the problem was solved, and what the solution was. Even the first chapter was highly illuminating.

Re: Ask HN: Math books like SICP?

#42

Post by kliao »

randomknowledge wrote: post #13
kliao wrote: post #5

Earlier quoted context omitted.

Echo the above. Pairing little Rudin with a more user-friendly book like Understanding Analysis by Abbott is a great way to learn the material if you get stuck.

Personally I would recommend mathematical analysis by Pugh. Goes into as much depth as Rudin, but more approachable and a great selection of exercises.

I like Pugh too. All three are sitting on my bookshelf :). Coming from very little formal math training, and trying to self-study analysis, I would bounce from Rudin if I got stuck, go to Abbott for a confidence boost, and try out some Pugh for a different viewpoint. Pugh might have been just right in terms of rigor and accessibility.

Re: Ask HN: Math books like SICP?

#43

Post by nextos »

randomknowledge wrote: post #13
kliao wrote: post #5

Earlier quoted context omitted.

Echo the above. Pairing little Rudin with a more user-friendly book like Understanding Analysis by Abbott is a great way to learn the material if you get stuck.

Personally I would recommend mathematical analysis by Pugh. Goes into as much depth as Rudin, but more approachable and a great selection of exercises.

I was under the impression that Pugh, while more approachable, was also much more difficult. Especially with regards to the exercises.

Re: Ask HN: Math books like SICP?

#44

Post by learc83 »

Jugurtha wrote: post #35

Well, I don't know how it goes over there, but here in Algeria, Engineers go through two common years (after which they chose a specialty in the third year, and then, in the fourth and fifth year, a specialty of specialty). All Engineers go through both years, except Computer Science who don't do the common second year and they directly go to Computer Science. In these two years, everyone goes through this (maybe it'…

>Also, most tests are designed in a way that even if you have the answer sheet right next to you, it still takes you more time to copy the answers than the time of the exam itself.

So the test is impossible then? If you don't even have time to copy the answers how can you possibly have time to work out the problems?

Re: Ask HN: Math books like SICP?

#45

Post by Jugurtha »

learc83 wrote: post #44
Jugurtha wrote: post #35

Well, I don't know how it goes over there, but here in Algeria, Engineers go through two common years (after which they chose a specialty in the third year, and then, in the fourth and fifth year, a specialty of specialty). All Engineers go through both years, except Computer Science who don't do the common second year and they directly go to Computer Science. In these two years, everyone goes through this (maybe it'…

>Also, most tests are designed in a way that even if you have the answer sheet right next to you, it still takes you more time to copy the answers than the time of the exam itself. So the test is impossible then? If you don't even have time to copy the answers how can you possibly have time to work out the problems?

You don't have time to do "all of it".

For instance, in Control Systems .. We get a problem to design a system with certain characteristics. You then have to do Z transform, etc. Then design correction to match what you're asked for (a certain overshoot max, phase, etc).

Which involves a lot of matrice multiplication (Pontryagin, optimal control). Big matrices multiplied(and elements aren't numbers, they're bits of transfer functions. But I replace them with letters and double indices, many students recopy the same expression all the way :) ).

Or your design an RST control (polynomial, much, much complex than PID).

All of this takes a lot of time to write and requires a lot of concentration (if you screw up just one element in a matrix, all ensuing is wrong and gets you nothing, so you have to be rigorous and not the day-dreaming type).

And you end up pretty much not doing some part of the thing, which is something most students don't find frustrating, since most of them wouldn't touch a part of it anyway (they haven't studied it, they don't understand it, or something else).

They're not designed like that by some sadistic tendency, it's just some stuff that needs to go down the exam..

Although I remember a teacher who told us as he gave us the exam sheet: "Don't bother looking at the verso". Meaning "You'd be happy if you only did the recto to get your 10/20". It was a deliberate move.

And in addition, it's mostly end of year exams that are like that (content from the whole year). And not all modules are like this. Some are calculation intensive and next step is dependant on current step, so making a mistake in the beginning is "fatal".

But then again, I find the exam thingy slightly ... well, let's not even go there.

Re: Ask HN: Math books like SICP?

#46

Post by hf »

oskarth wrote: post #38

Not the same type of book, but you could do a lot worse than reading through Mathematics: Its Content, Methods and Meaning , by M. A. Lavrent’ev, A. D. Aleksandrov, A. N. Kolmogorov. It's an amazing book which gives a mathematical (but not rigorous in the sense of proofs etc.) overview of most of mathematics. http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

Absolutely astounding: I have been looking for this book ever since I pored over it in the Wolfson Reading Room in Manchester Central Library 5 years ago. I didn't take down the authors' names, though, referring to it as "that yellow mathematics book" then and ever since.

I credit that book with much if not all my mathematical insight.

Thank you.

(Just seeing that cover leaves me all tear-eyed, reminiscing over that wonderfully irresponsible time.)

Re: Ask HN: Math books like SICP?

#47

Post by oskarth »

hf wrote: post #46
oskarth wrote: post #38

Not the same type of book, but you could do a lot worse than reading through Mathematics: Its Content, Methods and Meaning , by M. A. Lavrent’ev, A. D. Aleksandrov, A. N. Kolmogorov. It's an amazing book which gives a mathematical (but not rigorous in the sense of proofs etc.) overview of most of mathematics. http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

Absolutely astounding: I have been looking for this book ever since I pored over it in the Wolfson Reading Room in Manchester Central Library 5 years ago. I didn't take down the authors' names, though, referring to it as "that yellow mathematics book" then and ever since. I credit that book with much if not all my mathematical insight. Thank you. (Just seeing that cover leaves me all tear-eyed, reminiscing over that…

Glad to help. Amazing that an off-hand comment can have so much impact on a human being across the globe. I've certainly been on the other side of it several times before.

Re: Ask HN: Math books like SICP?

#48

Post by dobbsbob »

nextos wrote: post #39
krick wrote: post #25

Earlier quoted context omitted.

Eh, I was thinking about something else, actually. What you listed are taught in every CS program, aren't they? It isn't what I imagined when I heard "rigorous" at all. Topology, number theory, abstract algebra (I mean, real one, not CS-course basics), statistics, tensor analysis? Isn't that "undergrad math"? For things like Set theory/combinatorics/logic basics I'd recommend Rosen's "Discrete Math and Applications"[…

Thanks. I have already covered those topics during my CS undergrad. But I'm trying to redo some things at a much higher level. Hence the comparison with SICP, which is far from a regular introductory book. In the same vein, a course with Axler & Rudin is far more advanced than a standard one.

http://ocw.mit.edu/courses/mathematics/ find a course(s) that covers what you're looking for, write a blog and call it Structural Interpretation Of Undergrad Math and pick the book chapters and lectures that go into depth like SICP does (:

Re: Ask HN: Math books like SICP?

#49

Post by htns »

The Princeton Companion to Mathematics [1] is good if you want to gawk at the breadth and depth of the field. For actual education I would just suggest looking at a math department's syllabus, e.g. at http://ocw.mit.edu/. As a CS grad you should start with analysis, as that's probably your most looming dark spot.

My warning as a math student is that a lot of book recommendations are just a tad bit elitist. Don't stick with a single book too long if it isn't cutting it for self-study. Exercises are good.

[1] http://press.princeton.edu/titles/8350.html

Re: Ask HN: Math books like SICP?

#50

Post by jimmaswell »

Jugurtha wrote: post #35

Well, I don't know how it goes over there, but here in Algeria, Engineers go through two common years (after which they chose a specialty in the third year, and then, in the fourth and fifth year, a specialty of specialty). All Engineers go through both years, except Computer Science who don't do the common second year and they directly go to Computer Science. In these two years, everyone goes through this (maybe it'…

you have to retake Algebra even if you did it in high school?
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