Intereting Posts

Does this integral have a closed form or asymptotic expansion? $\int_0^\infty \frac{\sin(\beta u)}{1+u^\alpha} du$
Non-constructive axiom of infinity
Stuff which squares to $-1$ in the quaternions, thinking geometrically.
Differential equations and Fourier and Laplace transforms
Double Factorial: Number of possibilities to partition a set of $2n$ items into $n$ pairs
Is arithmetic with infinite numbers fictitious?
Unitary operator is identity
What do I need to know to understand the Riemann hypothesis
Non-associative, non-commutative binary operation with a identity
Markov property question
Can we prove the Cauchy-Riemann equations using the matrix form of a complex number?
$G_{\delta}$ sets in locally compact Hausdorff or complete metric space are Baire spaces
What's the probability that an NFL team with a given win/loss record makes the playoffs?
How do we show every linear transformation which is not bijective is the difference of bijective linear transforms?
Two covering spaces covering each other are equivalent?

First, I’m not trying to make this sound like a “poor-me” story. I understand fully that every decision I’ve made leading to this is my fault. I am genuinely looking for advice.

So, I am a high school student who is a sophomore and feel I have developed an interest in mathematics a bit late. As an elementary and even middle school student, I was always not paying attention in most math classes because they didn’t grab my interest. I think the reason for this is because most of my teachers were “old-fashioned” and didn’t really bother to explain the awesome things you can do with math. So on my end of things, I only saw manipulating numbers which didn’t seem to productive to me. I have always had a deep interest in computers and how they work (you can see where this is going most likely); So, upon entering my freshman year of high school I developed a passion for computer programming. I like a good challenge as well as creating things and this is the area where I really began to excel. Now realizing that large portions of math are required to major in computer science, I am beginning to worry a bit. A large amount of people I meet automatically assume I am good at math, and I feel sort of guilty for wasting those years of my life barely paying attention. Currently I am beginning to enjoy math, though.

I feel that most math teachers don’t capture the interest of the students because they don’t show the engineering side of things when it comes to math. I love creating original things and have been told I am very creative. I would like to use that creativity and produce creations using math, but I think I’m a bit behind.

- Math GRE Subject Exam
- What's the right moment to learn Set Theory?
- Which topics of mathematics should I study?
- I need help finding a rigorous precalculus textbook
- Can I get a PhD in Stochastic Analysis given this limited background?
- What am I losing if I decide to perform all math by computer?

My math final is tomorrow, so I’m rather stressed out. I suppose the actual questions in this post would be

- What are some good math study methods?
- Advice as to what I should do this summer to strengthen my math skills?

Thank you, I appreciate the time you take to help me with answers.

- What is the probability that GCD of $(a,b)$ is $b$?
- What are some strong algebraic number theory PhD programs?
- What are some good ways to get children excited about math?
- Math GRE Subject Exam
- Good way to learn Ramsey Theory
- Is math built on assumptions?
- Albert, Bernard and Cheryl popular question (Please comment on my theory)
- Examples of mathematical induction
- How to do well on Math Olympiads
- Why teach linear algebra before abstract algebra?

You might want to read this post on how to study math: it’s about good study methods /strategies for math. There are some great contributions/answers to that question.

Second, it is **never** too late to begin anew. Though you may feel like you’ve wasted “years” of your life, you’ve still got lots of time, and it seems you’ve got the motivation to build your math skills and explore your interests further and prepare for college. While it will take discipline to get up to speed and continue in math, and lots of persistence and patience, be sure to dabble in what excites you about math. Explore and have fun with math!.

Wish you the best, and welcome to the wonderful world of mathematics!

Okay, I have a bit of experience that other people here may not: I’m in almost the exact same situation as you.

I’m currently 16 and I discovered my love for mathematics back when I was 13. If you’re just discovering this at 15 or 16, don’t worry a bit. There is no need to worry. I am not a prodigy, and I can tell you that the majority of mathematics you’ve ‘missed’ is equivalent to about 3 weeks of studying. Truth be told, I have learned very little academic knowledge from school. Partially, this is my fault. However, primarily, I feel this is the fault of my state’s education system.

I bet you’re not in a very different situation! So, here’s what I recommend to you as a teen talking to another teen: Do what you love. You clearly love CS, eh? Okay, well, to go far in CS, you’ll need to truly understand the mathematics behind computers. But, before you can conquer that, you’ll need to master your basics (all high school subjects and a few undergrad subjects) in order to get a flavor for mathematics.

So, here is exactly what I think you should do: Make A’s in your classes (all of them—you seem smart enough to do that), study for the ACT and SAT (the most important portion for you, right now, being mathematics), participate in any academic extracurriculars (academic team?), study mathematics in your free time (!!!), and enroll in college math classes if you are capable.

Now, why do I recommend these things? I have done every single one of these things. I cannot tell you how surprising it is to truly and honestly study for the ACT and SAT. You learn in the most concrete way that you really don’t know a lot. By studying those two tests alone very rigorously, I learned a lot of concepts that I hadn’t seen before. The added bonus is that their questions are formatted so beautifully mathematically speaking that they help you learn the concepts so much quicker and easier. In general, there is always a beautiful method to solve any question they have and its beauty makes the learning process so much easier.

Here’s the importance of these things and how I would suggest doing them chronologically speaking:

- Studying in your free time
- Make A’s in all your classes
- Study for the ACT and SAT (as well as other school tests: e.g. PLAN and PSAT)
- Academic extracurriculars
- Enroll in extra college classes

As a final note, relax! Your life hasn’t been decided yet, and it won’t be for quite some time. However, don’t let this make you lazy. Let this inspire you to be amazing. That’s how I approach life. ðŸ™‚

Don’t feel too bad about ‘wasting time’ up till now. Most people don’t know any math, and few are good at it. You shouldn’t get down on yourself for being behind.

Instead, do the productive thing: problems. A thousand, thousand problems, from whichever disciplines of math you can find. The old adage that “Math is not a spectator sport” is very true. Reading math books and trying to understand will help some, but the only real way to learn math is to *actually do math.*

This site is good not just because you can ask more experienced people for help, but also because it gives you a venue to look at a variety of math problems. I learn a lot by trying to answer other people’s questions, even when I don’t know the answers right away.

In conclusion, solid, certifiable, genuine practice is the most important thing. Whether you get it from the internet or from books is up to you. Just find a topic you like, get disciplined, and finish what you start: *do problems.*

Khan Academy

Khan Academy is a non-profit organization that has a lot of instructional videos on you-tube and practice problems on their site. It helped me get through physics and calculus.

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- Normality is not hereditary
- Can an odd number $n$ divide $2^n-1$?
- Differential Equation – $y'=|y|+1, y(0)=0$
- Book about the foundation of math?
- How many possible DAGs are there with $n$ vertices
- $F:C\to D$, $G:D\to E$, $G$ has an adjoint, $F$ is fully faithful and for each $Z$ there is $X$ s.t. $F(X) = H(G(Z))$: Does $F$ has an adjoint?
- Reduction formulae