Before university next year, I need to teach myself advanced mathematics. I am far behind my peers and I don't want to struggle in university with basic concepts. I feel cheated in my math education so I am taking it into my own hands. As I plan to major in Economics, a strong background in calculus and other advanced topics is needed for success. Thus, I am calling all math wizzes to help a 16 year old who struggles with math.. How did you become proficient in math? What methods did you use to teach yourself? Content wise, how accomplished is your knowledge in mathematics and specifically how was that knowledge imparted upon you? What topics do I need to learn before next year? Vector and dots, matricies, logs, multivariable calculus, derivatives, and sequences.. how can I teach myself that? Here is what i DO know: Arithmetic(Division, Subtraction, multiplication, addition) Fractions, ratios, decimals Basic Number theory Basic Probability Permutations Basic Geometry: Area and perimeter of squares, trapezoids, circles, triangles, pentagons.. and all other polygons. Surface area and volume of all three dimensional shapes 30, 60, 90 and 45-45-90 right triangles Pythagorean Theorem Herons Formula Angles and angle relationships Basic and intermediate algebra: Factoring Function decompression, and operations Quadratic Equation Solving equations Simplifying all expressions exponential growth and decay Compound interest Imaginary Numbers, Square Roots, and exponents Graphing on the X, Y plane for all polynomials of a higher degree Finding the zeros of a polynomial of the nth degree Finding Slope, Slope intercept, y=mx+b Basic grasp on logarithms Solving system of equations via substitution Conic Sections: Equation of parabola, circle, hyperbola, and ellipse Basic grasp on limits Polynomial division

As someone who had struggled with math in early high school years (had C,D grades for 2 years) I decided that I would take the final exam no matter what and go study IT. Probably the most effective decision is to hire a personal teacher. Save your time, save your nerves and don't study things you won't need (get a trainer that knows nowadays university math requirements). If you decide not to hire a trainer, start with the basics. If you have a gap in your education - you can have a lot of problems in the future, so I strongly suggest you repeat all basic math program up to high school and learn your weak points. I was doing very fine in maths for first undergraduate year (advanced maths) but then I found out about drugs... Just remember - math is 90% of individual work.

i think at age 16 you really only need to know algebra. vectors/calculus/statistics is really the next step above that and you'll learn that all in college. everything you just listed looks good enough as it is for someone that just got out of high school. if you really wanna learn more math on your own though, i think wikipedia usually explains the concepts pretty well. you can also try to find out what courses you'll be taking and get the syllabus so you'll know exactly what to expect fun fact: if you know order of operations, you're ahead of 43% of this forum

I have actually dealt with your exact problem. Depending on the school you plan to attend the maximum you would be expected to know is entry level calculus; limits,derivatives, and intro to integrals.... If you look around the internet you should be able to find a lecture series called "Math Tutor". They were extremely helpful to me. Also, once you watch a lecture you must do many problems related to the topic. Problems, problems, problems.... You seem like an intelligent young man to be entering college at 16 so a (x)weeks of videos + (y) problems= confident freshman!! ; )... Keep it up! The hard work will pay off!

I taught calculus a long time ago in less than 1 semester to high school seniors using a review book for calculus students. It was really the simplest presentation. I don't live in the U.S. any more so i can't recommend what is good now. It might have been a barron's review book

Personally I was not very good at Math.. but the older I grew the more I could understand it correctly. One more thing that helped me to understand the basic logic of math, is programming.