# How to excel at math?

I know this question has been asked at least a hundred times earlier but before you mark this as duplicate please read this cause I seriously need some professional help here.

I'm a 15 year old kid who is pretty good at all other subject expect math. I am considered as smart but being self aware that I am not smart cause I am only just above average at math. I am a curious kid and I always was. I don't know where it went wrong but I failed somewhere.

Let me tell you something about my past. I started pre school at 4. I wasn't taught properly by my parents or family at home the only piece of education I got was from my school which was little less than four hours daily. I don't know if you guys are taught at home when you were young but in my local it it doesn't work like that every kid is taught from home more than that of school. But I remember that I was able to read and write way before than friends. I didn't care for math till recently because I was not challenged by it,I wasn't able to conceive it practical purpose which was clearly my teachers' failure I always ask my teacher "What this is used for ?" and she would answer "don't care about it". As I said am pretty curious and I think about everything so deeply, that's how I learn things.

I didn't attend school that much when I was young so I missed some basic arithmetic and I wouldn't ask anyone if had a doubt,I just pretended I knew it. I was always interested in science, especially physics I realised that it needed math so I started studying math last year even though I didn't like it. I also got interested in computer science recently and it need math too. So I've been pushing myself into studying it but it too obvious and I think it won't help studying if I don't love what I am doing.

I definitely got better at math recently cause I was terrible before. I got better at reasoning and problem solving lately but when it's from I syllabus I kinda fail. My teacher is good but she ain't the best,she just gives us many examples while not teaching a single bit of theory at all. I can't learn something clearly without knowing its meaning. Now let me compare my marks in math and other subjects,if I get 95 in science or any other subject, I would've gotten 85 in math. I don't know what's wrong with me, Am I math anxious or am I just stupid? As I mentioned above,I am kinda improving at math but i feel like it's not enough. I can go on and on but this is already longer than what I expected and I don't wanna make it tedious. I hope you will give me advices which would literally change my life cause I couldn't think of a career without mathematics.

• I read it as it is but others won't be so kind, seeing a wall of text incoming they will close the question without reading a single line ! – A---B Oct 13 '17 at 16:16
• How much maths you know ? Calculus ? – A---B Oct 13 '17 at 16:18
• @A---B yeah I know :( – nihaljp Oct 13 '17 at 16:20
• What makes you think you are stupid because you have $85%$ on maths? This is a good grade? – user370967 Oct 13 '17 at 16:21
• @awkward I just started reading A mind for numbers – nihaljp Oct 15 '17 at 10:41

I'm not sure whether people on this site (myself included) can give you better advice than people at school who know more about you than you have been able to summarize in your Question. So here are some things to think about. Perhaps take some as advice. Perhaps ignore others.

(1) I'm not sure whether starting to learn calculus at 15 is the best choice. Calculus may go better when you know some trigonometry and analytic geometry--and maybe patch a few gaps in your algebra.

(2) As you encounter things in math classes or independent reading that you don't understand, try to figure out if there are gaps in your background that may account for the difficulty and how you can go back and fill in the gaps.

(3) Because you're interested in uses of math in addition to theory, maybe look into aspects of physics, computation, statistics, and probability where math that interests you is used for various purposes.

(4) Think about the mechanics of solving problems: Here are a couple of suggestions to get you started. (a) Given the equation of a line and the coordinates of a point that is not on the line, can you compute the shortest distance from the point to the line? (b) Can you figure out the sum of this series? $1 + 1/2 + 1/4 + 1/8 + \cdots .$ (c) Given the equation of a parabola, can you figure out whether it crosses the x-axis? (d) What points in the plane satisfy $|x|+|y| \le 1?$ You might look on this site for other problems and solutions.

(5) When you run into an interesting math problem you can't solve, consider posting it on this site. Say what you have tried and what is puzzling you. Explain that it's for self-study, not a homework assignment. Maybe someone will give you an interesting and helpful answer.

(6) If there is a library at your school or in your town with some math books, consider browsing around to see if you can find interesting topics at your math level. I think books are more reliable sources of worthwhile math ideas than most stuff on the Internet.

(7) There are some books available online for free that are written by very good mathematicians who write well. One of them is Grinstead and Snell: Intro to Probability, which has interesting historical notes and doesn't require calculus. The PDF of the whole book is available free on the Dartmouth website. Maybe other people on this site can suggest other free (or inexpensive) books that might worth looking at.

(8) If you keep finding new math topics that interest you and keep patching gaps in the old ones, I think one day you may be advising others how to excel in math.

• That's a pretty good advice. Wish I had some kind of map for studying math step by step – nihaljp Nov 9 '17 at 20:18
• Btw I can answer the first three but not the last because I hadn't been taught that yet. I am good at leaning new things but not sure where to start with – nihaljp Nov 9 '17 at 20:22
• Do you know about absolute values? Question (d) is similar to asking what $(x,y)$ points satisfy $x^2 + y^2 \le 1,$ which is the points in a circle of unit radius with center at the origin $(0,0).$ // Those particular problems aren't important, but that you can answer (a)-(c) does tell a bit about your background. // The point is to be on the lookout for similar problems and learn from solving them. // A step-by-step guide should come after discussion with someone who knows you pretty well. // Wishing you success in your study of math. – BruceET Nov 10 '17 at 3:33
• maybe I should request for a map in another question – nihaljp Nov 14 '17 at 12:33
• Seems difficult to recommend a useful personal study outline working at a distance and not knowing more about you than fits in a web page. – BruceET Nov 14 '17 at 17:03

I think you should try to solve various math problems which involve elementary level of calculus algebra trignometry, etc. And trust me if will start loving math math will start loving you. Do problems and discuss them with instructor or here at math SE. If you want you can connect with me also. I am pursuing MS in mathematics. Will love to help you. And yes don't be grades oriented. If you love math then only you get best grades. And believe me math will help you to achieve number of milestones.

• Thanks for the support. I've been saying the same thing for a long time " I love math but math don't love me" – nihaljp Oct 13 '17 at 16:37
• How can you say that? Any example – ChiragMittal Oct 13 '17 at 16:42
• Please accept my answer. – ChiragMittal Oct 13 '17 at 16:42
• @ChiragMittal Don't force anyone to accept an answer. This is bad policy. – user370967 Oct 13 '17 at 17:26
• Sorry it will not happen again – ChiragMittal Oct 13 '17 at 17:30