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Online Education apps

17 points

·
25th Nov 2011

Well, here are some video lectures by Harvard on Abstract Algebra. They use the 1st edition of Artin's "Algebra" as the class text, if you happen to have it and want to follow along. I really would recommend getting your hands on a copy and doing all of the homework assigned for the class. Only then can you begin to learn it.

Harvey Mudd College has an excellent video lecture series on Real Analysis (Lecture 21 is missing from the playlist as it had to be recorded in a later semester, so you'll have to go on their channel to watch that one). The textbook used for this course is "Principles of Mathematical Analysis" by Walter Rudin (affectionately called Baby Rudin by many Analysts since Rudin also has "Real and Complex Analysis", Big Rudin), covering chapters 1-5.

I'm currently using Harvard's video lectures to keep myself busy over the holidays and to help with my goal of completing Artin in this semester. I wish they had video lectures for Algebra II (which finishes Artin) online, but I can't complain about such high quality free education. :) I'll be using the Harvey Mudd lectures for next semester when I plan on tackling Baby Rudin.

4 points

·
21st May 2015

I can recommend coursera - I liked it quite a bit.

MIT is also good, and Khan Academy is great for math/science, not so much for other things. I also dig Harvard's e-learning initiative.

4 points

·
16th Nov 2014

There are many online resources that you can use for free. MIT, Harvard, and Khan Academy (although I have no experience with Khan Academy).

3 points

·
14th Oct 2016

I assume by "Advanced Calculus" you are actually referring to Real Analysis (going through Calculus by way of proving every element of calculus using epsilon and delta proofs). If that is what you mean, then I can tell you that these are USUALLY the most difficult courses for math majors who are inexperienced with the concept of writing proofs. I would avoid those if you are looking for an "easy" class. It is a rare student who finds this easy.

History of Math is fascinating and I highly recommend it. The actual mathematics in the class is generally low level, but learning about the history is eye-opening. I ended up taking 2 more Math History courses for fun after taking my first.

I love Number Theory and Abstract Algebra, and I found both of those topics easy. HOWEVER...there are many people who don't feel that way. It seems to be a matter of what easily clicks for you...do you "get it" easily or not? I got it easily. Some others don't. Try a few of the videos here to see if it seems interesting to you: AbstractAlgebra

Probability and also Statistics are pretty easy if you've taken Calc II. Taking Statistics is also something that everyone should do in this day and age. It can really open up doors for you if you can deal with data in a meaningful manner.

3 points

·
30th Jan 2015

Try some coding before you quit your job. You may hate it or simply be unable to do it. It requires a certain kind of thinking to be comfortable doing it and to get really good at it.

Harvard has a free, online computer science introduction/course thing. I'm not sure how far it goes, but it would be a great way to get your feet wet and see if it's really for you. If you're comfortable with the material, I say go for it.

http://www.extension.harvard.edu/open-learning-initiative/intensive-introduction-computer-science

3 points

·
25th Jan 2014

This is a mostly standard second course in Algebra. It follows the second half of Artin's book, and more or less picks up where this course ends.

3 points

·
28th Feb 2012

Here are some links that have vids on abstract algebra but I have not watched them.

http://www.uccs.edu/~math/vidarchive.html

http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

I found the above links from this link.

http://www.infocobuild.com/education/audio-video-courses/mathematics/mathematics.html

Enjoy!

2 points

·
13th Apr 2015

About a third of the way down this UReddit course starts on Group Theory. I think it's a really good course that has videos, problems sets and solutions that explain the concepts in really simple terms: http://mathdoctorbob.org/UReddit.html

I'm also going through the lectures here: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

The lectures there teach Abstract Algebra under the basis that you have a good understanding of Linear Algebra. So the lecturer shows how the abstract concepts map to something you might be more familiar with.

Finally, the WikiBooks entry on Abstract Algebra is quite terse, but act as a good check to see if you are understanding the concepts: http://en.wikibooks.org/wiki/Abstract_Algebra

2 points

·
19th Mar 2015

Per your comment about not having studied linear algebra, I'd suggest that it would be advantageous for you to have some familiarity with the subject before going on to tackle abstract algebra. Strang is good, and his various OpenCourseWare lecture series are an excellent resource for someone new to the subject.

(Since you're into programming, I'd also mention that Prof. Philip Klein of Brown University has a free Python-based course available at Coursera called Coding the Matrix which is pretty fun. I wouldn't recommend the course as a standalone resource to learning linear algebra -- it's not intended to be a comprehensive introduction to the subject -- but you might find the course to be rewarding in conjunction with some more traditional study. If you're an experienced programmer, you'll probably breeze through it)

For a solid text, I'd recommend Artin's Algebra. It's very well written and the presentation has a strong geometric flavor. The problems in the book are also very good and quite challenging. I'd further recommend Prof. Gross' Harvard video lecture series from his Abstract Algebra course, which is available free here: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra ; his course uses Artin and problem sets are posted at the above site(though solutions are not).

Finally, I'd recommend that you avoid trying to take on a category-theoretic approach to abstract algebra for now. Once you've gotten a bit more algebra under your belt you'll be in a good place to pick up a copy of Lang's Algebra and the motivation for a category-theoretic approach will probably be more clear.

2 points

·
6th Feb 2015

I was in exactly the same boat.

Honestly, just watch these. The course is very self-contained, just hard.

You can also get the textbook ahead of time, Dummit and Foote's Abstract Algebra. I think they always use this book for 347, and even if they don't it is still a fly as fuck tome.

2 points

·
20th Nov 2014

Algebra: I think Artin is by far the best first text. It's a bit tough, but work through carefully and I think it's much more rewarding than any other introductory algebra books I've seen (Gallian, Herstein's two books). You can follow Dick Gross' great Harvard lectures here for additional insight: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra. Another book I like, but is quite outdated is MacLane and Birkhoff's A Survey of Modern Algebra (outdated is not too big of a deal for an introduction, especially if you plan on going through a more advanced and modern text in the future). Dummit & Foote is also a great text: it's presented in a clear, readable way in my opinion, but the sheer amount of material is a bit overwhelming and can make some parts rather dry. Lots of examples throughout the chapters though, which is very nice. It's rare to find such an encyclopedic text that's accessible to undergrads.

For differential equations, Tenenbaum's ODEs for more elementary stuff, and Arnold's ODEs for a more abstract presentation. I've never used any others, but Tenenbaum was useful to me starting out and Arnold's is one of my favorite books of all time.

For Linear Algebra, I'm actually a big fan of Axler, but I can understand why some don't like it. I don't think it's just a style preference thing though: I think everyone at some point SHOULD become comfortable with his treatment and presentation. But my favorite for undergraduate linear algebra is actually a standard text -- Hoffman and Kunze. Supplementing that with the Vector Space sections in Algebra books like Dummit and Foote is also fruitful. Learning linear algebra very well is very important for any mathematician, and linear algebra is one of the most important tools in every field I've come across, so it's good to know it well.

2 points

·
30th Apr 2014

http://www.extension.harvard.edu/open-learning-initiative

Harvard does offer free classes, Not to students but to any one who has the internet. and Stanford : https://opensource.stanford.edu/ ....And MIT : http://ocw.mit.edu/index.htm

I still think its bad to charge money for knowledge but there are clearly people who are trying to do the right thing here.

2 points

·
24th Jul 2012

You can see the existing videos for Harvard CS50 and MIT 6.00 (or 6.00SC) to get an idea of what each course might offer.

2 points

·
22nd Apr 2012

Agreed. And for abstract algebra in particular, Harvard has something similar I don't know what else they have but it's worth checking.

2 points

·
18th Feb 2012

The Harvard open learning initiative has a great abstract algebra course taught by Benedict Gross that uses Artin. He's a great professor, Artin is a great book and, best of all, the course is free.

2 points

·
20th Jan 2012

Personally I would recommend just picking up some quality books for topics you are likely to see in your first couple of years at university and start learning ahead.

For calculus I believe Spivak and Apostle are considered the best. I'm not so sure about linear algebra, but something that builds from vector spaces up is imo the best way to learn it. Abstract algebra is another thing you could start getting your hands dirty with, I'm not sure about an elementary introduction to that, there's some nice video lectures here.

If you insist on a book which gives a non-rigorous introduction to various parts of mathematics, you can't go past the Princeton companion to mathematics.

2 points

·
5th Dec 2011

Depends. Do you have anything you're looking towards being able to do? Just general logical and reasoning, or what?

Hey, check that out, free college course! http://www.extension.harvard.edu/open-learning-initiative Scroll down for the "Intensive Introduction to Computer Science"

2 points

·
22nd Nov 2011

Hey cultic_raider,

I'm basically watching Harvard lectures found here: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

and then using Wikipedia for extra information on the topic, things I don't understand/they didn't explain thoroughly.

2 points

·
21st Nov 2011

>OnlineEducation caters exclusively to students participating in the classes listed below.

Shouldn't it cater to all froms of free higher education online? If it's only about the Stanford classes it prob should stay as /r/StanfordOnline.../r/OnlineEducation should be a reddit where people can share resources for free online education regardless of source IMO ( like Harvard's open learning initiative etc)

1 point

·
9th Feb 2017

The most popular youtube video series is these lectures at Harvard the instructor follows Artin's book. You can also find this lecture series by James Cook, who uses Gallian's text (5th ed). You can also find some stuff on MIT OCW which also follows Artin's book (because it is Michael Artin teaching the course).

1 point

·
29th Dec 2015

I agree that it has some value, but as far as what sort of compensation you should receive for having it, the rate is low. Where it does hold value is getting people interested in technology.

It's only good if the person taking it doesn't have practical hardware/software administration. TIA tests, especially A+ can be a real joke. Some questions are moronic, others ask you the 15-character designation and transfer rate of a connector type that went extinct over a decade ago and traditionally goes by a simpler name.

I've been on the hiring side of the table for support jobs like you mention, generally people with A+ on their resume are like OP, high school aged, and have high school amounts of experience. The A+ won't get you a living wage unless you're interested and experienced beyond what it tests you on.

My advice to OP if they actually want to pursue IT, is take classes online, for __ free__. MIT and Harvard offer classes with more relevant computer science coursework.

1 point

·
7th Nov 2014

There are a few one-off courses that can be found online.

Harvard's Extension School has put up the course materials, including video, of Prof. Gross' Abstract Algebra course. (LINK)

Coursera has a free course on Functional Analysis running right now, which has videos, course notes and peer-graded homework problems(LINK). If you look through the course listings Coursera and edX.org, you'll be able to find a few other free online courses(calculus, linear and integer programming, signals and systems, Galois theory, and numerical methods for ODE's are some of the ones I've seen).

1 point

·
22nd Apr 2014

You might be interested in Benedict Gross's lectures from a Harvard course. They're also on YouTube. He's very clear and he does a great job of making the results seem interesting.

1 point

·
31st Mar 2014

Dr. Su's lectures on real analysis were very enjoyable as were Dr. Gross' videos on abstract algebra. Additionally, everything on MIT OCW.

1 point

·
9th Sep 2012

China: Traditions and Transformations is a class from Harvard. It looks interesting. I've also recently started listening to China History podcast, and I'd like to go on record as saying that Laszlo Montgomery is an okay dude.

1 point

·
26th Jun 2012

Quotes are wrong. Lesson #1: TYPE IN CODE. You will learn a lot more that way. In my day we had a magazine called Compute! full of programs and I typed in every program. We didn't have copy and paste. That has served me very well in my life. After typing the same thing over and over you get muscle memory for the common stuff, giving your brain spare time to focus on what you are trying to express with your program, instead of focusing on how you express it in language xyz. You don't actually think about putting a period or a space in when you type english, coding is the same way. If you want to take short cuts and copy and paste, you are not going to learn nearly as quickly. You will make mistakes when you do that, sure, but you will learn from those mistakes by discovering what happens when you leave something out or fat finger a number. You will make mistakes for the rest of your life, you have to be able to identify them. Let this be a lesson to you. Also note this will be easier when you have an instructor and other classmates. If you want a taste of what your class will be like, Harvard has a decent CS50 up on the web. TYPE THAT SHIT IN BOY.