23 votes

When do college students learn rigorous proofs?

From day one. In my experience in Germany, proofs are taken seriously from day one, or even before that. We had a voluntary prep course before the first semester that was half a repetition of calculus ...
13 votes
Accepted

When do college students learn rigorous proofs?

In my experience (U.S.), that's on the boundary between 2nd and 3rd year -- either the end of sophomore year or the start of junior year. Two years ago I did a survey of Associate in Science (2-year) ...
10 votes

What should I learn after calculus?

Take your time Andrew, don't worry so much about classes. Learn Python and solve your calculus problems with it. Learn R and solve your Stats problems with it. If you can do this by the end of your ...
  • 984
10 votes

Soft question: take complex analysis or cryptology?

I will vote for complex analysis. The main theme of complex analysis is that differentiable complex functions are incredibly rigid, which is completely different from the behaviour of differentiable ...
9 votes

Introductory real analysis before or after introductory abstract algebra?

Despite the names of these fields, as a student I found real analysis more abstract than abstract algebra: real analysis was less real and more abstract to me than abstract algebra. I don't think I ...
8 votes

Introductory real analysis before or after introductory abstract algebra?

Is 'at the same time' an option? I mean, by junior year, math majors should be taking at least two math classes per semester, right? When I was an undergraduate at Penn State, these two courses were ...
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8 votes

Soft question: take complex analysis or cryptology?

An argument can be made in favor of Cryptography, not because it is more fundamental than Complex Analysis, or more beautiful, but because: (1) You have not yet taken Number Theory, and you will ...
7 votes

When do college students learn rigorous proofs?

From my experience in French Classes Préparatoires, we learn proofs during year one without a specific course about it, just while we learn calculus and linear algebra, starting on day one (we ...
  • 171
6 votes

When do college students learn rigorous proofs?

This answer is meant to supplement Daniel R. Collins' answer, which is excellent—my goal is to draw a little more distinction between the "levels" of education and training in the US. Short ...
  • 6,681
6 votes

When do college students learn rigorous proofs?

In the UK, students usually learn proofs in the first year of a mathematics degree. My experience is similar to Sumyrda's answer. They also gain some exposure to proof techniques before university in ...
  • 1,605
4 votes

What should I learn after calculus?

This same question has arisen at my current institution even earlier (i.e., after AP Calculus AB). The traditional next course after the Calculus is Real Analysis (constructing the real numbers in one ...
3 votes

What should I learn after calculus?

What you likely will not have experienced after Calculus and Statistics is: proofs. At most institutions, both Discrete Math and Linear Algebra introduce, and may even concentrate on, proofs. The same ...
3 votes

When do college students learn rigorous proofs?

At my school, UIUC (https://illinois.edu/), we have a dedicated proofs course for CS majors (CS 173: Discrete Mathematics) and a dedicated proofs course for math majors (Math 347: Fundamental ...
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3 votes

When do college students learn rigorous proofs?

I'm in Scotland and did rigorous proofs in the first year of my degree (Physics) as I sat the full first year maths syllabus. Although, in the final year of high school we were introduced to some ...
3 votes

When do college students learn rigorous proofs?

Naval Academy has their proofs class spring of sophomore year. It is required for either applied math or pure math. https://www.usna.edu/MathDept/_files/documents/majorMatrices/SMA.pdf https://www....
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2 votes

When do college students learn rigorous proofs?

I can only speak to my personal experience, but during my time in Undergrad there was a dedicated proof writing class ("Introduction to Higher Mathematics") that was coded as a 330 course. ...
2 votes

What should I learn after calculus?

That depends on what you're interested in. If you're thinking about biology or chemistry as a career, differential equations would be a good choice. If you're interest is in computer science then I ...
  • 1,163
2 votes
Accepted

The sequence of chapters

Seem you have two problems. The students resistance and the misunderstandings of which chapter you are referring to. To overcome the student's resistance, suggest that they (the students) are part ...
  • 7,163
2 votes

What should I learn after calculus?

As a number theorist I am biased, but I think a conjecture-proof study of elementary number theory could be a good place to start. Many summer programs for mathematically-inclined high school ...
  • 2,956
1 vote
Accepted

Complex Variables for Engineers versus Ordinary Differential Equations with Linear Algebra difficulty

The difficulty of the courses depends on the content and execution of the courses in question, and as such, the question does not have an answer.
  • 4,832
1 vote

The sequence of chapters

You use the phrase "chapter[s] in my course" (as opposed to the book), which makes no sense linguistically. I would recommend that you find some other way of expressing what you're trying to say. This ...
1 vote

The sequence of chapters

In my experience, this hasn't been an explicit reason for students finding the subject harder. In fact, it was quite common to teach subjects (not just maths) in a different order than what is given ...
  • 516
1 vote

What should I learn after calculus?

Also consider linear algebra. Given your interests one emphasizing matrix manipulation rather than theory is preferable, for now at least. P.s. In general, when accelerating in high school try to ...
  • 113
1 vote

What should I learn after calculus?

I think you should focus on learning practical and interesting skills that will help you to get a coding job. For example, how about learning how to code in C#, Java or even Javascript? Coding is a ...
1 vote

Soft question: take complex analysis or cryptology?

My advice is to take complex analysis, but a more applied version (weak on proofs, strong on contour integration). Just based on your question and what you said about yourself, I think you will enjoy ...
  • 365

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