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This is an advanced real analysis course, in which we will study sequences of functions, numerical series and generalized integrals.
The objective of the course is to master the following concepts:
Simple and uniform convergence of sequences of functions.
The different modes of convergence of a real or complex numerical series, the Cauchy product of two series.
The different modes of convergence of an improper integral.
Schedule: 24 hours of CM + 36 hours of TD per semester (2 hrs CM + 3hrs TD per week)
Assessment Style:
Smith Students say...
What did you gain from this course?
"As this was my first mathematics course taken in French, I learned a lot of vocabulary for math terms, as well as how to write out a solution to a math problem that is « bien rédigé », and how to discuss math problems.
I learned a lot about improper integrals, sequences, and series, namely how to determine their nature (convergence/divergence), and how to effectively approach these types of problems.
More generally speaking, I got a sense for how French students approach their CM and TD courses, regarding levels of attentiveness and participation."
Did the professor welcome exchange students in the course?
"No."
What do you wish you'd known before taking the course?
"The course was harder/more overwhelming at the beginning because I felt there was a lot of catching up I had to do in order to get where the French students were with their level of knowledge (and the last time I had dealt with the topics directly related to this course was in high school). Thus I wish I had spent some time brushing up a bit on those calculus topics before the semester started so I had more of the basis and didn't have to do that and learn the new material at once. I also wish I was able to make a bit more time, especially towards the end of the semester, to study my notes and practice problems, because that time outside of class was definitely essential to my learning. This course is intended to go towards my analysis requirement for the math major, so it most resembles MTH 281 (Introduction to Analysis)."
To whom would you recommend this course?
"A math student with a good basis in calculus who wants to continue their learning in calculus/analysis. I would also say, despite not being calculus classes, it helped me to have already taken MTH 153 (Introduction to Discrete Mathematics) and MTH 233 (An Introduction to Modern Algebra), for approaching problems and mathematical reasoning."
Words to describe this course: challenging, productive, analytical, helpful
JYA student 2023-2024
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