Quick 1-paragraph summary of all of math

  • Thread starter Fletcher
  • Start date
In summary, the conversation discusses the most efficient way to self-learn higher level mathematics, starting with a calculus level knowledge. The suggested topics include logic and foundations, algebra, number theory, algebraic and complex geometry, geometry, topology, Lie groups and Lie algebras, analysis, operator algebras and functional analysis, ordinary differential equations and dynamical systems, partial differential equations, mathematical physics, probability and statistics, combinatorics, mathematical aspects of computer science, numerical analysis and scientific computing, control theory and optimization, applications of mathematics in the sciences, mathematics education, and the history of mathematics. It is mentioned that the best path of study depends on one's goals with math, and if one wants to become a mathematician,
  • #1
Fletcher
25
0
Go!

Actually I want to pose this hypothetical question:

If you wanted to self-learn most of the higher level mathematics most efficiently, starting with a calculus level knowledge, how would you go about doing it?
 
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  • #2
* 01. Logic and Foundations
* 02. Algebra
* 03. Number Theory
* 04. Algebraic and Complex Geometry
* 05. Geometry
* 06. Topology
* 07. Lie Groups and Lie Algebras
* 08. Analysis
* 09. Operator Algebras and Functional Analysis
* 10. Ordinary Differential Equations and Dynamical Systems
* 11. Partial Differential Equations
* 12. Mathematical Physics
* 13. Probability and Statistics
* 14. Combinatorics
* 15. Mathematical Aspects of Computer Science
* 16. Numerical Analysis and Scientific Computing
* 17. Control Theory and Optimization
* 18. Applications of Mathematics in the Sciences
* 19. Mathematics Education and Popularization of Mathematics
* 20. History of Mathematics

The best path of study depends on your goals with Math. If you want to be a Mathematician, you can't go wrong with Abstract Algebra and Analysis (advanced calculus).
 
  • #3
Crosson,

Is there a book, understandable to a Mathematics B.S., which overviews the topics you list?
 

FAQ: Quick 1-paragraph summary of all of math

What is the purpose of math?

Math is the study of numbers, quantities, and shapes. It helps us understand and solve real-world problems, make predictions, and develop critical thinking skills.

What are the main branches of math?

The main branches of math include arithmetic, algebra, geometry, trigonometry, calculus, and statistics.

How does math relate to everyday life?

Math is used in everyday life in various ways, such as managing money, cooking, measuring, telling time, and understanding patterns and relationships.

What are some key concepts in math?

Some key concepts in math include numbers, operations, equations, functions, geometry, and probability.

How can I improve my math skills?

To improve your math skills, you can practice regularly, seek help from a tutor or teacher, use online resources, and approach problems with a positive attitude and persistence.

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