Academic Guidance What and how to study

Feb 2014
Hi I am 28 and I decided to try math again. I used to be a good math student until 9 th grade. But than it got really really bad. I absolutely fell behind and math became a nightmare for me.
I think that my failure was due to psychological factors and a very fast paced curriculum.
Now I want to go back to math because when I was a child I liked it quite a lot and recently I discovered my interest in computers. I've never tried programming but maybe in future I will.
I also enjoy watching numberphile videos because they show beauty of mathematics.
I would also try to prove myself I am not so stupid as I've thought since high-school.
What do you suggest I study, where should I start and what to focus on?
Last week I started pre algebra on khan academy and I already knew about 3/4 of it, the rest is new to me. I think it would be necessary to take algebra after that.
What should I study after algebra? I enjoy geometry like constructing shapes when given angles and calculating area of something. I also enjoy learning about patterns and properties of numbers when numberphile explains it.
I really suck at functions and I never understood them. I had real problems working with abstract letters when I had no idea what they meant.
I know there are many areas of mathematics but I don't know what they deal with. Can you give me an advice how to build my basics and what topic should I study on more advanced level?
My purpose is mainly to be able to see elegance and beauty and to train my brain. Just maybe I might need it in future for programming but I am not sure if I will ever go that direction.
Thank you.
Oct 2013
New York, USA
The high school math I learned was algebra, then geometry, then trigonometry. Here are chapter titles for each:

1. Sequential Math I: 14 chapters
Numbers and Variables- Basic concepts
Logic and Truth Tables
Solving Linear Equations
Solving Literal Equations and inequalities
Operations With Polynomials
Operations With Algebraic Fractions
Operations With Irrational Numbers
Fundament Ideas In Geometry
Comparing and Measuring Geometric Figures
Equations of Lines; Introduction to Transformations
Solving Systems of Equations Inequalities

2. Sequential Math II: 12 chapters
Mathematical Systems
Polynomials and Algebraic Fractions
Solving Linear and Quadratic Equations
Basic Geometric Terms and Proving Triangles Congruent
Parallel Lines and Triangles
Special Quarilaterals and Polygons
Similar and Right Triangles
Coordinate Geometry
Locus and Constructions
Quadratic Equations In Two Variables
Probability and Combinations

3. Sequential Math III: 10 chapters
Review and Extension of Algebraic Methods
Review and Extension of Equation Solving
Complex Numbers
Relations, Functions, and Transformations
Exponential and Logarithmic Functions
Trigonometric Functions: The General Angle
Trigonometric Identities, Equations, and Formulas
Solving Triangles
Bernoulli Experiments, the Binomial Theorem, and the Normal Curve
Feb 2020
I have also encountered the same problem just like you. A topic taught in high school does not necessarily mean they are higher than the topic that was taught in lower level of education. In my case, I was taught two dimensional geometry and three dimensional geometry in elementary school, but I don't think that topic is mathematically considered "higher" in level than the pre calculus that was taught in highschool.
It would be better if you know which math area specifically linked to the computer programming. One of My childhood hobby was drawing. I could even draw in my leisure. Because of that, I have been looking for the mathematical area that deals with drawing and I have found it is geometry that is arguably linked to drawing. The persective drawing arguably follows some geometric principles. In addition to that, I have another hobby: origami and I have found that some say it is also linked with geometry since it deals with how to construct shapes using a sheet of paper.
In my story, I began finding it difficult to understand math when I was in highschool. The topic of math that we learnt that I have managed to recall were: Trigonometric functions, radical, exponent, and differential and integral.
The most important of learning is the continuation despite failure. Failure can make us lose our confidence. If we fail in a spesific topic of math, probably we can still thrive in the other topic. Previous mathematicians can't have mastered all topics of math known now and the term mathematics is actually a union of separated topics discovered by different persons. Euclid discovered Euclidean geometry and his geometry has been unified within the subject to which we are introduced as Mathematics. Calculus was discovered by Leibniz and Newton and their independent discoveries have also been unified with the same subject to which we are introduced as Mathematics. As informed by Wikipedia, Even Newton, was assessed lack of understanding in Euclidean Geometry.
It is reported that in his examination for a scholarship at Trinity, to which he was elected on 28 April 1664, he was examined in Euclid by Dr Isaac Barrow, who was disappointed in Newton's lack of knowledge of the subject.
Early life of Isaac Newton - Wikipedia

It would be better not to aim to master all of mathematical topic known nowadays but instead to selectively learn which topic of math that you are naturally interested in and probably took note on which topic we are bad at only for self evaluation.
Last edited: