• Four Science Terps Awarded 2025 Goldwater Scholarships

    Four undergraduates in the University of Maryland’s College of Computer, Mathematical, and Natural Sciences (CMNS) have been awarded 2025 scholarships by the Barry Goldwater Scholarship and Excellence in Education Foundation, which encourages students to pursue advanced study and research careers in the sciences, engineering and mathematics.  Over the last 16 years, UMD’s nominations… Read More

  • Announcing the Winners of the Frontiers of Science Awards

    Congratulations to our colleagues who won the 2025 Frontiers of Science Award: - Dan Cristofaro-Gardiner, for his join paper with Humbler and Seyfaddini: “Proof of the simplicity conjecture”, Annals of Mathematics 2024. - Dima Dolgopyat & Adam Kanigowski, for their joint paper with Federico Rodriguez Hertz: “Exponential mixing implies Bernoulli”, Annals of Mathematics… Read More

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    Maryland Global, published a great interview with our visiting professor (and diplomat), Qendrim Gashi. The interview is available at https://marylandglobal.umd.edu/about/news/math-olympiads-diplomacy-meet-visiting-math-professor-qendrim-gashi Read More

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    Eugenia Brin, a Russian immigrant and retired NASA scientist who, with her family of accomplished Terps, became an important benefactor of the University of Maryland, died on Dec. 3, 2024. She was 76 years old. The rest of the article can be read here: https://cmns.umd.edu/news-events/news/eugenia-brin-1948-2024 Read More
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Description

A rigorous analysis of functions of one variable.

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241); and minimum grade of C- in MATH310


Level of Rigor

Advanced


Sample Textbooks

Advanced Calculus, by P.M. Fitzpatrick

Working Analysis, by J. Cooper


Applications

Chemistry, computer science, economics, engineering, physics, astronomy, mathematics


If you like this course, you might also consider the following courses

MATH 411, MATH 437, MATH464


Additional Notes

Students interested in grad school in AMSC should consider this course

Students interested in grad school in MATH should strongly consider this course

Students interested in grad school in STAT should strongly consider this course  

Topics: Chapters 1-4 and 6-9 from Advanced Calculus, by P.M. Fitzpatrick:

1.  Axioms and properties of real numbers

2.  Convergent and divergent sequences. Closed and compact sets.

3.  Continuous and uniformly continuous functions

4.  Differentiation

6.  Integration (Darboux integral): Two Fundamental Theorems

7.  Integration by parts and substitution (Sections 7.2) and Approximation of integrals: Trapezoidal, Simpson's Rules (section 7.4)

8.  Approximation by Taylor polynomials (not including 8.7: Weierstrass Approximation Theorem)

9.  Sequences and Series of Functions.

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