How to learn higher mathematics? Where to beginn?

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Discussion Overview

The discussion revolves around how to begin learning higher mathematics, particularly from a foundational level. Participants explore various resources and approaches to understanding mathematical concepts beyond basic school mathematics, including proofs and advanced topics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses a desire to move beyond school mathematics and seeks guidance on starting higher mathematics, mentioning their current focus on learning mathematical proofs.
  • Another participant inquires whether the original poster has covered transcendental functions, suggesting a potential area of study.
  • A suggestion is made to explore MIT's open course site for mathematics courses that include video and audio resources.
  • Another participant recommends working through Spivak's calculus as a valuable resource for learning higher mathematics.
  • Two participants request lists of theorems and postulates for high school level geometry, indicating a need for systematic learning resources for students in special education.
  • One participant mentions a specific geometry textbook (Prentice-Hall from 2003 or 2004) that may contain useful listings of theorems and postulates.

Areas of Agreement / Disagreement

Participants present various resources and approaches without a clear consensus on the best starting point for learning higher mathematics. Multiple views and suggestions remain, indicating that the discussion is unresolved.

Contextual Notes

Some participants express uncertainty about the prerequisites for higher mathematics, such as the necessity of understanding transcendental functions or the effectiveness of specific textbooks. The discussion reflects varying levels of familiarity with mathematical concepts and resources.

Who May Find This Useful

This discussion may be useful for individuals interested in transitioning from basic to higher mathematics, educators seeking resources for students, and those looking for structured learning materials in mathematics.

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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