/sci/ - Science & Math

>>9688316
Which one is the best among those? I want a book that will help me ace the IMC. In /sci/'s Wiki they recommend 3:

- Topics in Algebra, by Herstein
- Algebra, by Artin
- Basic Algebra I and II, by Jacobson

>>9688349
Sorry for that, I messed up in the formatting, but well, you kinda get the point.

>>9688349
>>9688353
I doubt anyone has read all three of those books, I'd say just go with Algebra by Artin

>>9688375
Does it have really hard exercises?

>>9688316
what is the IMC?
if it's anything like a qual, you probably want to start with Jacobson II

>>9688421
It's the Internation Mathematics Competition for University Students.

http://www.imc-math.org.uk/

What is a qual?

>>9688316
The best one for the IMC is "Homological Algebra" by Cartan and Eilenberg.

>>9688501
Why though? That one is not even on /sci/'s wiki, how can I trust you? What makes that book better than the others?

>>9688427
if it's for undergrad, then standard undergrad-fare texts should be fine (jacobson I, artin, or if you have the time and like encyclodpedias, dummit & foote)
homological algebra is algebra for engineers, don't be fooled

>>9688510
>That one is not even on /sci/'s wiki
Most sane people would consider that to be a good thing.
>What makes that book better than the others?
Clarity of exposition and the amount of material treated. It's pretty good for the IMC specifically since it focuses on the classical side of algebra aided with geometric/topological intuition.

>>9688515
>homological algebra is algebra for engineers
Then it's the perfect thing to learn for the I"M"C.

>>9688515
okay, just looked at the last year's test
i think the questions are pretty straightforward and they don't appear especially challenging, so light studying may be enough. then again, these things always look simpler once you're past them - it looks like it could be fun for you
if you want a good text for preparing for math competitions, try "Putnam and Beyond"

>>9688316
Fraleigh if you are just starting.

>>9688533
Isn't Putnam and Beyong for High School students?

>>9688909
it's aimed at undergraduates, and suitable for the vast majority of undergraduates, who are interested in problem-solving/competition. in particular, it is supposed to aid students in preparing for the Putnam exam. that's exam for undergrads which has a median score of very few points - in 2016, median score was 1

problem solving?
Sounds like you need "Methods of Homological Algebra" by Gelfand and Manin
it's only 350 pages and very helpful for competitions

>>9688316
>http://4chan-science.wikia.com/wiki/Mathematics#First_Year_Algebra_.28Undergrad.29
>Herstein's Topics takes a fairly conventional approach to the subject while Artin's book does things in a rather unique and geometrical way. While both are well written texts on their own, but pairing them is very useful.

>>9689152
homological algebra is a meme. op should just look at any book on universal algebra and just be done with it

>>9688316
I definitely do NOT recommend Artin.

It’s a good reference, but a terrible book to learn from. It’s structured in such a way that only someone who already has a good grasp of abstract algebra will really benefit from the way it’s presented and from the exercises.

You know how most books have chapters that are divided into sections (e.g., 5.1, 5.2, etc), and that the exercises at the end of the chapter are grouped in the same way so that they correspond to the material in the respective section? Well, Artin’s book does this, but most of the exercises still require you to understand material presented later in the same chapter.

That is, if you are trying to solve a problem in section 5.1, chances are that you will will need to understand materials presented in later sections, like 5.3, in order to do the problem.

The result is that you always have to read THE ENTIRE CHAPTER and understand all the material before even attempting the most basic problems at the end of the chapter. Not all of the exercises are like this, but a surprising amount.
Every once in awhile, you’ll even come across a problem that requires knowledge of material that isn’t even introduced until later chapters, not just later sections in the same chapter.

So if you already understand a good amount of abstract algebra, either from watching lectures, having read another text or having previously taken a class on it, then Artin is fine.
If you’re learning it for the first time ever, then Artin is fucking awful.

>>9689226
>homological algebra is a meme.
Who isn't these days?

>>9689216
OP here, holy shit really thanks for that anon, didn't see that part in the Wiki.

Is Stillwell's' Elements of Algebra' a good primer on abstract algebra?

>>9689290
norman wildberger

>>9688316
the suggestions I got from some old professors I know were

"A First Course in Abstract Algebra" by John Fraleigh
"Contemporary Abstract Algebra" by Joseph Gallian

I've been running through Gallian chapter by chapter and I really like it. It is very readable, and there is a full solutions manual out there.

>>9689439
These are both brainlet books for cs majors.

>>9689288
Artin was used in my first abstract algebra class and I don't ever remember needing later material to solve exercises.

>>9689860
Yeah but that’s the difference, you had a lecturer to supplement the book. I tried to use it for self study, and it’s not self-contained for that kind of learning.

>>9689880
I knew kids that self studied Artin and skipped to the graduate algebra class with Lang.

I think you just lacked the mathematical maturity for it and are blaming the book for expecting too much of you.

>>9689439
Gallian reads like a high school textbook and is literally not worth the paper it's printed on. Your professors think you are a brainlet if they recommended you those.

>>9689860
Are you a genius or something?

>>9689889
>says he self-studied the topic for the first time using the book
>”you lacked the mathematical maturity”

That’s literally his point, it’s not a good place to start.

>>9689373
pls respond

>>9689967
You don't need to study baby tier algebra/analysis to gain mathematical maturity for algebra/analysis. There are other easier subjects in math.

>>9689977
Completely agree. By the time you're at abstract algebra you should be comfortable with rigour or something has gone horribly wrong in your education.

>>9689892
>tfw they're not "my professors"
both of them are math professors for 40+ years. one is my uncle, he said he used "Topics in Algebra" by Herstein to teach one class, and "Algebra" by Hungerford for the other.
but he said "i'm an analyst, and it's actually my colleague X's field so probably has better suggestions"
>X recommends fraleigh, gallian, and of course his own textbook he wrote 35 years ago which will go unnamed ITT
>tfw your own friends and family deemed you a brainlet and gave you high school tier books
murdering myself tonight anon thx for helping me see the truth

>>9689977
What would be 'baby tier' Analysis?

are you brainlets seriously just now learning algebra? I learned that shit in 8th grade lmao

>>9690083

The topics in Gallian are the same as in any other undergrad algebra text. The fact that it is easy to read and understand is a plus.

Hungerford is by far the best algebra text for more advanced students.

Your dad knows the score.

>>9690098
Rudin's Principles of Mathematical Analysis.

>>9690214
Was this supposed to be a joke? If you think Rudin's 'baby tier' then what book would you recommend that is 'high level'?

>>9689288
Why do math elitist recommend Artin for first exposure to Algebra, and Spivak/Rudin for first exposure to Calculus? I almost am at the point I completely ignore any recommendations

>>9690218
>t. brainlet

>>9690098
Gaughan, Abbott, Bartle, Ross, Spivak

>>9690217
Papa Rudin and Grandpa Rudin, obviously.

>>9689856
>>9690192
and my degree in EE
so they know i'm a brainlet not a real mathematician
they probably laughed and said i can't handle a real book