Math 330: Advanced Calculus 1 (Fall, 2020)

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Professor Youngjoon Hong:

Email: yhong2 AT sdsu DOT edu
Office hours: see the Syllabus below.


Course Links:

Useful Links:

Course Description:

This course is a proofs-based, rigorous examination of many of the results used in a first semester Calculus class. The purpose of this course is to provide students with the opportunity to develop mastery of rigorous thinking and the techniques needed to develop rigorous approximations in Calculus. The techniques and problem solving skills developed in this course are crucial to future success in courses in mathematics or in the teaching of mathematics since they form the core of how one thinks in a rigorously mathematical way.


Course Prerequisites:

Math 245 and 254 or Math 342A with a grade of C or better in each course.

Course Outline:

  • Practice using logical quantifiers and language to rigorously express statements in Calculus.
  • Practice using the language of set theory to rigorously formulate mathematical expressions over a variety of different kinds of sets.
  • Practice deriving estimates and bounds for transcendental and rational functions.
  • Develop techniques for the estimation of the error in common approximations.
  • Use the formal definition of sequential limits to prove that various sequences do or do not have limits.
  • Use the formal definition of continuous limits to prove the limiting behavior of functions.
  • Use the formal definition of Cauchy convergence and the concept of completeness to establish the existence of rigorous limits.
  • Use the formal definition of continuity to prove that various transcendental and rational functions are or are not continuous.
  • Use the formal definition of differentiability to prove foundational results from Calculus and to prove when and where more complicated functions are or are not differentiable.

    Recommended Textbooks:

      Lecture notes + (optional) Advanced Calculus, Second Edition, by Patrick M. Fitzpatrick

    Students with Disabilities:

    If you are a student with a disability and believe you will need accommodations for this class, it is your responsibility to contact Student Ability Success Center (SASC) at (619)594-6473. To avoid any delay, please contact Student Ability Success Center as soon as possible. Please note that accommodations are not retroactive, and cannot be provided until an accommodation letter from SASC is received by the Professor.