Order of mathematical concepts

[MillerGenuine]

I have taken courses in math up to calculus 2, after which my math ambitions came to a quick hault. I would like to pick it back up and attempt to casually learn some math on my free time. So I would like to know the sequence/order of math concepts that someone would normally take at a given school. I will start this off to give an example and show what i know so far, anyone feel free to further elaborate my list or branch out on your own. My goal is to be able to conceptually understand all mathematical concepts, even if i cannot caculate. thanks ahead.

• algebra
• geometry
• trigonometry
• pre calculus
• calculus1: limits, derrivatives
• Calculus 2: integration, techniques of integration, volumes, divergence and convergence
• Calculus 3: ...?
• ...

 

[micromass]

After calc II, there is no longer a linear connection between topics. That is, you can study a lot of independent things. Some things you can do:

- Linear algebra: matrices, vector spaces, transformation. After this, you can take abstract algebra

- Calculus III: studies multivariable derivatives and integrals. After this, you can study vector calculus or calculus on manifolds.

- Analysis: You can study real analysis (which is just the rigorous version of calculus), then complex analysis or functional analysis or ...

- Discrete mathematics and/or logic: studies discrete systems like graphs or generating functions. Logic studie axiomatic systems. The two topics are fairly different, but a first course usually combines the two.

All these things are very much proof-based. So be sure to know proofs before embarking on your journey.

 

[HallsofIvy]

Calculus 3 typically extends the concepts of Calculus 1 and 2 to higher dimensions, dealing with functions from Rⁿ to R or from R to Rⁿ. "Analysis" deals with the theory behind Calculus. After that would come "Linear Algebra", "Abstract Algebra", "Differential Equations", "Partial Differential Equations", "Complex Analysis", "Functional Analysis", ...

Of course, there is no standard "ordering" of most of those.

 

[mathwonk]

arithmetic, algebra 1, logic, geometry, linear algebra 1, elementary number theory, calculus, diff eq 1, adv calc, elementary differential geometry, abstract algebra 1, algebraic plane curves, linear algebra 2, real analysis 1, topology 1, complex analysis 1.

now you can take grad algebra, grad real analysis, grad complex analysis, grad number theory, grad algebraic topology, basic algebraic geometry, grad differential geometry, pde, all in any order you like.

 

[Matrix0]

I would first like to commend you for your interest in continuing to learn and expand your understanding of mathematics. The order of mathematical concepts can vary depending on the curriculum of the school or institution, but I will provide a general sequence that is commonly followed.

1. Arithmetic - this is the foundation of all mathematical concepts and includes basic operations such as addition, subtraction, multiplication, and division.

2. Algebra - this builds upon arithmetic and introduces the concept of variables and equations.

3. Geometry - this branch of mathematics deals with the properties and relationships of shapes and figures.

4. Trigonometry - this involves the study of triangles and their properties, as well as the relationships between angles and sides.

5. Pre-calculus - this is an advanced level of algebra that includes topics such as functions, graphs, and logarithms.

6. Calculus - this is a branch of mathematics that deals with rates of change and includes topics such as derivatives, integrals, and limits. It is typically divided into three levels: Calculus 1, Calculus 2, and Calculus 3.

7. Linear Algebra - this branch of mathematics deals with vector spaces and linear transformations, and is often taken after Calculus 2.

8. Differential Equations - this involves the study of mathematical equations that describe how a quantity changes over time.

9. Statistics - this branch of mathematics deals with the collection, analysis, and interpretation of data.

10. Real Analysis - this is an advanced level of calculus that focuses on the rigorous mathematical foundations of calculus.

11. Abstract Algebra - this deals with algebraic structures such as groups, rings, and fields.

12. Number Theory - this is the study of integers and their properties, and is often considered the purest branch of mathematics.

Of course, this is not an exhaustive list and there are many other branches and subtopics of mathematics that one can explore. I would recommend starting with the fundamentals of arithmetic and algebra before moving on to more advanced topics. Additionally, it is important to practice and apply these concepts in order to truly understand them. Best of luck in your mathematical journey!