List of Mathematical Topics please!?

Question

I am a person who can teach myself almost anything.
I love mathematics and science, and preferably I would like to teach myself everything I can in Mathematics.
First off I need to go to the library and check out books on mathematical topics starting from the basics.
Can you please list all mathematical topics starting from basics and building upon the previous topic?
Thanks, P.S., if you have any tips on self-teaching mathematics, please share! Thanks!

Answer 1

I was a math major in college and here was my progression of classes:



Easier Classes:

Single Variable Calculus

Multi-Variable Calculus

Discrete Mathematics

Statistics



Middle Level:

Linear Algebra

Complex Variables

Differential Equations

Introduction to Geometry

Mathematical Modelling



Upper Level:

Number Theory

Modern (Abstract) Algebra

Analysis

Topography



My advice is to instead of checking out a textbook on multivariable calculus, look for the books written by mathematicians that explain these concepts more broadly. There's a lot of good books that give the big ideas without the complex math details.



However, if you do like those math details a great subject that doesn't require the breadth of math experience needed for differential equations is combinatorics. It is the study of counting things, which can actually be really interesting.



Good luck!

Answer 2

List Of Math Topics

Answer 3

Haha wow. Have fun learning ALL of math! The most basic, is of course, the concept of a number. The number 3 DOESN'T mean 3 sheep or 3 rocks or 3 cups or 3 miles or 3 seconds. But it's that thing those values all have in common. It's very abstract.



I think you are beyond those basics. I'm going to skip over multiplying and dividing whole numbers as well. But for ALL TOPICS, it is MEGA important to understand the CONCEPT first, and then how to do it.



The BIGGEST thing most people trip up on is fractions. Fractions come up EVERYWHERE. They become more and more complex, and mistakes are made later when the basics haven't been mastered.



Here I go . . .



Fractions: concept, add, subtract, divide, multiply

Algebra 1: variables, solving equations with variables, solving inequalities with variables (techniques include factoring and graphing)

Geometry: Pythagorean theorem, basic trig with right triangles, arc length concept

Alg 2: concept of a function, inverse functions, simultaneous equations, inequalities and absolute values, rational expressions, quadratic equations, exponents, logs

Precalc: Trigonometry, vectors

Calculus: Derivative, Integral, techniques of finding the antiderivative, the CONCEPT of the derivative and integral and how they connect



Math goes on forever. Calculus is considered the highest level fundamental math.

Answer 4

The order in which mathematics is usually taught is:

Elementary Math

Mid-Level Math

Algebra I

Geometry

Algebra II

Trigonometry ............}

Pre-Calculus Algebra } These go together

Calculus I

Calculus II

Calculus III

Linear Algebra

Bridge to Abstract Mathematics

Vector Calculus

Intermediate Analysis

Elementary Abstract Algebra

.

.

.





In that list you can put Differential Equations after Calc II, Statistics and Combinatorics after Calc II, and Topology after Vector Calc (not sure about the pre-req here). Also Geometry is in itself a huge part of mathematics so it is a very deep field. That's all I really know. For more details try searching for schools' mathematics curricula.

Answer 5

The best possible list for mathematical reading that I could suggest goes in this order:



Basic math: (order of operations, decimals, percents, ect...)



Algebra: (basic math with letters representing real numbers and everything about functions of real numbers...)



Geometry: (angles, shapes, area, surface area, volume, and a little trigonometry (great to have letters representing real numbers)...)



Trigonometry: (angles as a function of triangles and circles, trigonometric functions, inverse trigonometric functions, law of sines and cosines (need a firm grasp of algebra and geometry at this point)... )



Linear Algebra (metrics, solutions of linear equations, vectors... (you could use all of the above math that I have listed. Vectors are very useful which you will see later in 3D math)...)



Pre-Calculus: (More of the same math, but it works more on your algebraic and trigonometric skills (which is needed, because after this point it depends upon your level of mathematical ability)...)



2D Calculus: (yes, there is a 3D/ multi-D calculus) : (Limits, Differentiation, Optimization and mean value theorem, Integration(There is a TON of information and applications of integration), introductory differential equations, and the Infinite series (This may seem like a lot (which it is), but if you pay special attention to all of the previous math, Calculus may actually turn out to be not as hard as you think)...)



Multi-D calculus: (Vectors, Partial Differentiation, Multiple Integration, Vector valued functions and applications (You know 2D Calculus, you will know Multi-D calculus)...)



Differential Equations (Linear and Non-Linear Differential equations and techniques of finding solutions, including transformations. (Again, you know Calculus this will fall into place)...)



Vector Analysis: (More about vectors and transformations (This is where I start to not know much about the math involved (I am trying to read up on transformations))...)



Discrete Math: (Everything including complex numbers and complex analysis (hardest math I can think of)...)



Best tip I can give if you for self-teaching mathematics is take notes from the books, apply it to real-world problems as well as abstract problems, and be patience (math generally doesn't hit people like a brick in the head the first time they do a problem unless a ton of practice is taken).

Answer 6

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RE:

List of Mathematical Topics please!?

I am a person who can teach myself almost anything.

I love mathematics and science, and preferably I would like to teach myself everything I can in Mathematics.

First off I need to go to the library and check out books on mathematical topics starting from the basics.

Can you please list all...

Answer 7

I think this video will help a little. (his videos are awesome btw and it should help you with your studies)



http://www.youtube.com/watch?v=dsFQ9kM1qDs&feature=player_embedded

Answer 8

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