Fall Schedule 2010. Opinions and thoughts?

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Discussion Overview

The discussion revolves around a student's upcoming fall schedule, which includes courses in Applied Differential Equations, Number Theory, Foundations of Mathematics, and Advanced Calculus. Participants share their thoughts on the feasibility of taking all these classes simultaneously, particularly the challenges associated with Advanced Calculus and the Foundations of Mathematics course.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants express concern that taking Advanced Calculus I alongside Foundations of Mathematics may be overwhelming, especially for those without prior proof-based coursework.
  • Others suggest that the Foundations of Mathematics course is an introduction to higher mathematics and proofs, which could complicate the schedule.
  • A participant mentions their current enrollment in Linear Algebra I and plans to prepare for the fall by studying proof techniques.
  • Some argue that self-study may be necessary but caution that it could lead to frustration if the courses are taken concurrently without adequate preparation.
  • There is a suggestion that reading textbooks over the summer might be more beneficial than relying solely on a "how to do proofs" book.

Areas of Agreement / Disagreement

Participants generally agree that the proposed schedule is challenging and may not be advisable without a solid foundation in proof techniques. However, there is no consensus on whether the student should drop Advanced Calculus I or proceed with the full schedule.

Contextual Notes

Some participants note the importance of prior experience with proof-based classes, which may affect the student's ability to handle the proposed schedule. There are also varying opinions on the effectiveness of self-study methods in preparation for the courses.

Who May Find This Useful

Students considering similar course loads in mathematics or those seeking advice on balancing challenging subjects in higher education.

thethinker
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Hi, guys. This is my schedule for the coming up fall.

Appl Differential Equations I
Intro to Number Theory
Foundations of Math
Advanced Calculus I

I know it will be challenging. Do you think I should take all these classes at once or should I drop the Advanced Calculus I? Any thoughts or opinions would be appreciated. Thanks.
 
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thethinker said:
Hi, guys. This is my schedule for the coming up fall.

Appl Differential Equations I
Intro to Number Theory
Foundations of Math
Advanced Calculus I

I know it will be challenging. Do you think I should take all these classes at once or should I drop the Advanced Calculus I? Any thoughts or opinions would be appreciated. Thanks.

Is Advanced Calculus I a sort of introduction to analysis? And what is foundations of math?
 
Here's a description of each class:

MA 238 Applied Differential Equations I 3 credits
First order differential equations. Higher order linear differential equations. Systems of first order linear differential equations. Laplace Transforms. Methods for approximating solutions to first order differential equations. Applications. Students should have taken or be taking MA 227. Core Course.

MA 311 Introduction to Number Theory 3 credits
An introduction to classical number theory with a balance between theory and computation. Topics include mathematical induction, divisibility properties, properties of prime numbers, the theory of congruences, number theoretic functions, continued fractions

MA 320 Foundations of Mathematics (W) 3 credits
The students will develop facility with proofs through the study of logic and proof techniques as applied to various areas of mathematics. Topics include symbolic logic, proof techniques, relations, functions, and the structure of the number system.

MA 334 Advanced Calculus I 3 credits
This is the first of a two course sequence designed to provide students with the theoretical context of concepts encountered in MA 125 through MA 227. Topics covered include Completeness Axiom, sequences of real numbers, suprema and infima, Cauchy sequences, open sets and accumulation points in Euclidean space, completeness of Euclidean space, series of real numbers and vectors, compactness, Heine-Borel Theorem, connectedness, continuity, Extremum Theorem, Intermediate Value Theorem, differentiation of functions of one variable.
 
So basically MA 320 is an introduction to higher math - an introduction to proofs. Usually this type of class gives people trouble, much less taking it with an intro. analysis course and a rigorous number theory course. Not to mention, if you haven't had any proof-based classes yet, number theory and adv. calc. will be tough on their own. Your schedule is doable (I had a friend last semester do largely the same thing), but will be challenging. Have you talked with an adviser about it?
 
Newtime, thanks for the reply. I have talked to my adviser but it seemed that he doesn't know that much about advising based on our conversation, even if I could called it that. Currently, I'm taking Linear Algebra I and have been introduced to simple proofs. Also I'm planning to get the book, "How to Read and Do Proofs" by Solow in the summer to prepare for the fall classes. But from your experience, should I keep this schedule or change it?
 
I wouldn't take an intro to analysis course without first having Intro to Proof. Any decent introduction to analysis class is either going to move incredibly fast, or assume that you have a decent knowledge of proofs.

I guess If you're willing to do a lot of self-study, it may be possible to do, but it may also make you hate the subjects, even though if you had spread them out a little more, you might have actually enjoyed them.
 
jeffasinger said:
I wouldn't take an intro to analysis course without first having Intro to Proof. Any decent introduction to analysis class is either going to move incredibly fast, or assume that you have a decent knowledge of proofs.

I guess If you're willing to do a lot of self-study, it may be possible to do, but it may also make you hate the subjects, even though if you had spread them out a little more, you might have actually enjoyed them.

I'm going to strongly agree with this. That said, if you're set on doing this schedule, the best thing to do is not read a "how to do proofs" book as a method of self study but actually go through and read your textbooks this summer. Over the course of 3-4 months you should be able to finish the meat of most of them.
 
Thanks guys for the advices. I'm definitely going to take them into consideration before choosing my classes for the fall.
 

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