where to start if you lack basics?

Question

I've joined this forum for few weeks now and it amazes me that so many people are good at math. For me, I'm more of a history person rather than math person, so I hated math since I was young, not because math itself is bad, but because I thought math was not necessary in our daily lives and I wouldn't even use it when I grow up. Then after I joined this forum, I changed my mind and actually started to think that math is fun and it is the most essential part of our daily lives. I realized that everything is related to math, even history! Now, I want to start studying math but I lack kind of basics of math, and I don't know where to start from. I know basic algebras and just a bit of calculus. I'm afraid because since I'm already a grown up, my brain cannot follow the difficulties of math. Can you give me any tips on how to become good in math? Any personal story is appreciated.. Thanks a lot

Answer 1

First of all you will have to judge where you are in the grand scheme of things. I'd say get yourself steady with algebra and calculus first, you could do some probability on the side as well if you want. These 3 things will give you a pretty good foundation to take maths further.

There's a book called Thomas Calculus its often recommended for people starting calculus it will definitely cover everything you could want to know and then some more. I think your best bet though depending on your level is to look at a mathematics department website at a university or college and see what their recommended texts are for their first year calculus and core algebra modules. Sometimes lecturers will upload their lecture notes as pdfs and you can download them (just google module title lecture notes). They are obviously course specific and only contain what the lecturer wants to teach however.

For calculus look at: Functions - Domain, range, inverse, limits, continuity, derivatives. Differentiation - Chain/product/quotient rules, derivatives of standard functions (exponential, sin, cos etc.) Logarithms, L'hopital's rule, curve sketching, local extrema and asymptotics. Hyperbolic Functions Integration - Definite/indefinite integrals, Anti-derivatives, FTOC. Integration by parts, Integration by substitution. Parametric curves. Ordinary differential equations. Taylor series. Fourier series Functions of 2 variables. Partial differentiation. Double integrals.

Algebra: Basic set theory The number sets $\mathbb{R},\mathbb{C}$ etc proof by induction/contradiction/contrapositive [Understanding proofs is fundamental], iff, necessary, sufficient injections, surjections, bijections and function inverses vectors dot/cross products complex numbers FTOAlgebra Matrix algebra up to 3x3 (including finding inverse) reducing matrices to echelon form systems of linear equations linear independence eigenvalues and eigenvectors matrices that represent rotations and reflections in 2D/3D Basic groups

Once you have the foundations down I'd recommend studying some probability, statistics, linear algebra and some classical mechanics. If you are really set on taking maths far then you should also study real analysis. After this is where everything starts to get awesome (if it already wasn't). You can really decide what kind of mathematics you want to do, there's number theory, differential equations, complex analysis, more probability/statistics, multivariable/vector calculus, fluid dynamics, (groups rings and fields), quantum mechanics, special/general relativity, programming languages, the list is pretty much endless. Personally i'm all about the quantum mechanics, a lot of QFT recently.

One tip I'd say is never give up. Maths can seem very hard at times but when you finally understand a concept that can't be taken away from you. You'll look back at things you studied 6 months prior and it will all seem so much easier than what you are doing now. It just takes a bit of practice and some dedication to stick at it. If you are ever stuck you can just ask us as well ^^. Good luck and have fun!

Ill add some fundamentals to get you started later when im on my pc.

Answer 2

I'm 51 years old. I did some math in high school, but hadn't done anything but basic algebra (plus a little statistics) for 30 years.

4.5 years ago, at 47, I decided to go to college, and had to start back at nearly the beginning (Algebra II). I'm about to graduate with a minor in mathematics, and I'll be going to graduate school to get a master's in economics and applied mathematics.

I'll never be Euler, but if you keep an open mind and don't convince yourself you can't do it, you can do math.

I would start taking classes at your local community/junior college. The discipline and guidance will help a lot. I don't know where you're at, but the CC I went to has Alg. II, Trig, Calc I, II, and III, differential equations and linear algebra, which is 5/6 of the way to a math minor.