How to learn higher mathematics? Where to beginn?

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SUMMARY

The discussion centers on how to effectively learn higher mathematics, particularly for individuals with a foundational knowledge of school-level mathematics. The participant has begun with the book "100% Mathematical Proof" to grasp mathematical proofs, which is a solid starting point. Recommendations include utilizing MIT's OpenCourseWare for comprehensive math courses and studying "Spivak's Calculus" for a deeper understanding of calculus concepts. The importance of systematic learning through structured topics is emphasized, particularly for those transitioning from high school mathematics.

PREREQUISITES
  • Basic understanding of school-level mathematics including analysis, stochastics, and linear algebra.
  • Familiarity with mathematical proofs and their significance in higher mathematics.
  • Access to resources like MIT's OpenCourseWare for structured learning.
  • Knowledge of calculus fundamentals, particularly through texts like "Spivak's Calculus."
NEXT STEPS
  • Explore MIT's OpenCourseWare for mathematics courses to gain structured knowledge.
  • Study "Spivak's Calculus" to strengthen calculus skills and understanding.
  • Learn about mathematical proofs in depth to build a solid foundation for advanced topics.
  • Research modern high school geometry textbooks, such as the Prentice-Hall Geometry textbook, for systematic learning of theorems and postulates.
USEFUL FOR

Students transitioning from high school mathematics to higher-level mathematics, educators seeking resources for teaching advanced concepts, and anyone interested in developing a deeper understanding of mathematical proofs and calculus.

danov
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Hello, I am 18 years old and I am very interested in mathematics.

I have only knowlegde of school-matematics (school-Analysis, school-stochastics and a little bit school-linear Algebra) but that's not really interesting. Its basically memorising given methods to solve exercises instead of really understanding what is behind this methods.

So, basically my question is:

How can I learn higher Mathematics and where to beginn?

In fact I already started by learning mathematical proofs (book: 100% mathematical proof). Is it "right" to start with learning proofs? I just thought it would be good because Univerity Analysis/Algebra-books (like Widder) are very hard to understand for me with my school-knowledge.

What do you suggest?
 
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Have you covered your transcendental functions yet?
 
mmm have I got a site for you, check out MIT's open course site, here is a link to their math courses that have full video/audio:

http://ocw.mit.edu/OcwWeb/web/courses/av/index.htm#Mathematics
 
get a copy of spivak's calculus and work through it.
 
List

Does anyone have a list of Theorems and Postulates and the definitions for high school level geometry? I am an Instructional Aide in Spec. Ed. and one of my students is looking for one. Or if you can tell me where I can find one online. I've already been to 'Spark Notes.'
 


litendkns said:
Does anyone have a list of Theorems and Postulates and the definitions for high school level geometry? I am an Instructional Aide in Spec. Ed. and one of my students is looking for one. Or if you can tell me where I can find one online. I've already been to 'Spark Notes.'

An important feeling is that they need to be learned systematically with the normal flow of the course topics. Some modern h.s. Geometry books should have some listings. Look in the Prentiss-Hall Geometry textbook (I believe from year 2003 or 2004). The book is probably one of the best. Therein is found a listing of theorems, but I can not remember if a listing of postulates was also present.
 

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