Relearning Math: Comparing Resources for the Best Learning Experience

Hsopitalist said:

One last thing. I gave myself a year to do algebra, precalculus and trig. Starting with those two EdX courses made a HUGE difference there. Now I'm on to calculus I'm doing at least ten problems per day and the steady exposure really helps.

And I use a trig text by Lial. I've found it quite useful in explaining the really basic stuff.

Good luck and get to work! Keep us posted on your progress

That's basically what I'm doing right now. Going to try and get the bulk of the foundation laid out over the summer, and then try to keep it fresh in my brain during the school year.

I'd love to keep you guys posted on my progress. It'll be a good way to motivate myself to stay committed!

econreader said:

Well, trigonometry is the only one which is a bit like a textbook. It is still kind of short (but I guess the length is normal for a school textbook). Of course, Gelfand being one of the top mathematicians, one can still learn a lot from anything he writes. Same with Polya. I just wouldn't expect these books to replace read & drill from more conventional sources. I don't know much about precalculus books since I learned it while in secondary school, but you may want to check one of the books by Allendoerfer and Oakley which is often recommended here. I read their book as a refresher some time ago and I can confirm that it is awesome. Also, it's very cheap for a second hand copy.

Yes, I read the same book by Eccles as what you ordered. I was skeptical at first but it is actually quite good unlike some "introduction to proofs" books which are often superficial. I supplemented it with Norman Biggs' Discrete mathematics for a couple of topics, but since you have one by Rosen, you should be able to use it instead.

The books by Euclid are mind-blowing but will require a very serious commitment - so I personally put them aside till I have free time to study them. Same with Euler - it's fun to read a genius (and actually quite easy to follow this one), but he goes into topics which are not so immediately pressing to learn, so I'd keep it aside and turn to it for fun reading and use the time to focus on the shortest reading path to calculus.

I've seen the Allendoerfer and Oakley books go for very cheap second hand. But as MidgetDwarf said, I'm going to try to put a pause on any more purchases. If I can't get to a point where I feel like I'm ready for calculus with my current resources, I may have other things to worry about, haha.

I imagine the book by Eccles and Hammack's free proof book will be more than enough to get a better grasp on proofs. I should've mentioned that in first semester we did a couple weeks on proof by contrapositive, contradiction and mathematical induction. The thing is, between the rush of being back in school for the first time in a number of years, and not having had done math in nearly a decade, a lot of it was learned at a very shallow level. I plan to dive much deeper this time around.

The books by Euclid and Euler were part of the additional materials I purchased after I initially made this post. I don't expect to make them part of the core part of this curriculum. But I do think I'll get a lot out of them after finishing some of the material I mentioned in the first post. I plan on waiting to go through Euclid's books until I get a copy of Hartshorne to accompany it with. This probably won't be until next summer.

MidgetDwarf said:

I would hold off on buying any more sources. You have enough to last at least 2 years. The Gelfand book on trig is very neat, although it lacks problems/topics. But everything contained within it is lucid. There is a neat proof of the Pythagorean theorem, that is not so trivial. It uses some advanced Theorems about geometry. However, he dumbs it down that even a kid can understand. Although, the proof given in Gelfand is more intuitive than mathematical rigor. You have a pre-calculus book. Combine that with Gelfand, and you are good at intro trig. One can dive deeper, but I think its good enough.

This same proof was required in my Modern Geometry class, of course, the more rigorous proof. But the teacher explained it so confusing (we used his lecture notes) during a previous lecture. Needless to say, I was the only person in my class to understand and write a correct proof, since I seen the intuitive explanation in Gelfand 5 years prior.

Couldn't agree more. I got a bit carried away with this new found excitement.

You got me very excited for the trig book by Gelfand. I am curious about one thing though. Since there aren't any problems to practice with in it, do you think Cohen's Precalculus with Unit Circle Trigonometry will be enough practice to hammer home those concepts? My ignorance might show a bit here as I'm unaware if the trigonometry that Gelfand covers and the things covered in Cohen's book are different from each other.

Lastly, that's the thing with teaching. You can know the material inside out, forwards backwards. But that doesn't make you a great teacher. I imagine there's a reason why out of the endless list of publications out there, I see the same few authors get recommended over and over.

Yes. Teaching is an art. I have a very intelligent teacher (numerous publications). However, his lecture just goes over my head. He does try to explain it so that students understand.

But sometimes, while taking a bath or walking. Things click. I can replay some of his lectures by memory years later. So I don’t think he’s that bad. How do you like the books so far?

MidgetDwarf said:

Yes. Teaching is an art. I have a very intelligent teacher (numerous publications). However, his lecture just goes over my head. He does try to explain it so that students understand.

But sometimes, while taking a bath or walking. Things click. I can replay some of his lectures by memory years later. So I don’t think he’s that bad.How do you like the books so far?

Haha, I certainly didn't mean your teacher was bad. Sometimes being introduced to a new topic by a teacher who's extremely intelligent can be confusing. It's tough for them to put themselves in the students' shoes.

The books are great! So far I've only received the Gelfand books, Lang's Basic Mathematics, Euclid's books and Velleman's How to Prove It.

I'm working through Lang right now and it's exactly what I needed. With the rest of the shipments that are yet to come, I've got a very busy summer ahead of me!

I realize I'm late to this party but I would say my reaction to getting Velleman was ... meh. Daniel Solow's "How To Read And Do Proofs" is immensely superior in my opinion.