Prerequisites for real analysis?

[Tim92G]

I am returning to school, and I want to take a course in real analysis and abstract algebra this fall. I have been out of school for a year due to health reasons. The only math class I have credit for is Calc III, which I took first semester of my freshman year. I was enrolled in linear algebra and diff eq., but I had to withdraw from school early in the spring semester so I never got credit for them. I plan on taking a proficiency test to place out of diff eq., which I already know, and the introductory math proof writing course. I'm probably going to take the Linear Algebra again, because I feel I need a thorough review of it. My school doesn't list any prerequisites for the Analysis or abstract algebra sequence. You can only get into it by filling out a form at the mathematics department and receiving approval from the professor of the course.

 

[deekin]

This is how it works at my school. There is an "Intro to Analysis" class, which has the prereq of an "Intro to Proofs" class. Then there is "Mathematical Analysis 1", which uses baby Rudin, and the prereq is that "Intro to Analysis" class.

I think that if you are comfortable with writing proofs, for the most part, you will be fine. Maybe find out what book they are planning to use, this might help you see if you're prepared.

 

[Tim92G]

Thanks, I see that the book they use is Rudin's Principles of Mathematical Analysis. The book used for the abstract algebra course is Michael Artin; Algebra. Is Linear Algebra a prerequisite to Abstract Algebra, or could I take Part 1 of Abstract Algebra concurrently with the upper level Linear Algebra course?

 

[lurflurf]

Algebra can be taught including an introduction to linear algebra, parallel to linear algebra, or as a follow up to linear algebra. The Artin book uses more linear algebra than some others, but it is self contained (includes the linear algebra you need to know). The preface points out that the book does not require previous linear algebra, but if it is assumed it will be possible to skip or move quickly through the linear algebra to other topics.

 

[Matrix0]

It is great to hear that you are interested in taking a course in real analysis and abstract algebra this fall. Real analysis is a fundamental subject in mathematics that builds upon topics learned in calculus, while abstract algebra is a more abstract and advanced field of mathematics. In order to succeed in these courses, it is important to have a strong foundation in mathematics.

Based on the information provided, it seems like you have taken some introductory courses in calculus and linear algebra, which is a good start. However, it is recommended that students have a strong understanding of single and multivariable calculus, linear algebra, and basic proof writing before taking a course in real analysis. It is also helpful to have some exposure to topics in abstract algebra, such as group theory and ring theory.

Since you have taken Calc III and are planning on taking a proficiency test for differential equations, it seems like you have a good grasp of calculus. However, it is important to review and solidify your knowledge of these topics before diving into real analysis. Additionally, taking a course in linear algebra again can also be beneficial in preparing you for abstract algebra.

It is also worth mentioning that real analysis and abstract algebra are both proof-based courses. Therefore, it is important to have some experience with mathematical proof writing. It is great that you are planning on taking an introductory math proof writing course, as this will prepare you for the rigor and structure of these advanced courses.

It is important to note that every university may have different prerequisites for real analysis and abstract algebra. It is best to reach out to the mathematics department or the professor of the course to discuss your background and determine if you are ready for these courses. It is always better to have a strong foundation before taking on more advanced topics in mathematics.

I wish you all the best in your studies and hope that you are able to successfully complete the real analysis and abstract algebra sequence. These courses are challenging, but also incredibly rewarding, and I am confident that with your determination and hard work, you will excel in them.