How to learn higher mathematics? Where to beginn?

In summary, the conversation discusses a person's interest in higher mathematics and their question on how to learn it. They mention starting with mathematical proofs and suggest checking out MIT's open course site and using Spivak's calculus book. They also ask for a list of theorems and postulates for high school geometry, which can possibly be found in the Prentiss-Hall Geometry textbook.
  • #1
danov
12
0
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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  • #2
Have you covered your transcendental functions yet?
 
  • #3
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
 
  • #4
get a copy of spivak's calculus and work through it.
 
  • #5
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.'
 
  • #6


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.
 

1. How do I know if I am ready to learn higher mathematics?

Before beginning to learn higher mathematics, it is important to have a strong foundation in basic mathematics concepts such as algebra, geometry, and trigonometry. It is also helpful to have a good grasp of critical thinking and problem-solving skills. If you feel comfortable with these concepts and have a strong motivation to learn, you are ready to begin learning higher mathematics.

2. What topics should I start with when learning higher mathematics?

The first step in learning higher mathematics is to start with the fundamentals. This includes topics such as sets, functions, and basic mathematical reasoning. It is also important to have a solid understanding of calculus before moving on to more advanced topics such as linear algebra, differential equations, and abstract algebra.

3. What resources are available for learning higher mathematics?

There are many resources available for learning higher mathematics, including textbooks, online courses, and video lectures. It is important to choose resources that are appropriate for your learning style and level of understanding. You can also seek help from tutors or join study groups to enhance your learning experience.

4. How much time should I dedicate to learning higher mathematics?

Learning higher mathematics requires consistency and dedication. It is important to set aside a specific amount of time each day to study and practice. The amount of time will vary for each individual, but it is recommended to spend at least 1-2 hours per day on studying and practicing problems.

5. How can I apply higher mathematics in real life?

Higher mathematics is used in a variety of fields such as physics, engineering, economics, and computer science. It can also be applied in everyday situations, such as budgeting, analyzing data, and problem-solving. Learning higher mathematics can also improve critical thinking and analytical skills, which are valuable in many aspects of life.

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