Honors Mathematics A and B
MATH UN1207 – Honors Mathematics A is offered in the fall only. See the College Bulletin listing.
MATH UN1208 – Honors Mathematics B is offered in the spring only. See the College Bulletin listing.
Course Description
Honors Mathematics A and B form a rigorous, proof-based sequence in linear algebra and multivariable calculus. The sequence is intended for students with a strong calculus background, a serious interest in mathematics, and a desire to study the material at a deeper theoretical level.
The sequence is especially appropriate for prospective mathematics majors and students considering advanced coursework in mathematics. It fulfills the linear algebra requirement for the mathematics major.
Honors Mathematics B may not be taken without first completing Honors Mathematics A.
Both courses include mandatory recitation sections. Students are expected to attend both the lectures and the assigned recitations.
Prerequisites and Preparation
Students should have a strong background in single-variable calculus and be prepared for a fast-paced course emphasizing abstract reasoning and mathematical proofs. Students uncertain whether the sequence is appropriate for them should review the department’s calculus placement guidelines and consult the instructor or the Calculus Director, George Dragomir.
Textbooks and Course Materials
Instructors typically use one of the following:
- Tom M. Apostol, Calculus, Volume II, 2nd edition. See the publisher’s page.
- Friedman’s notes for Honors Mathematics.
The main topics covered in the sequence are generally consistent from year to year, but the organization, emphasis, level of abstraction, examples, and treatment of the material may vary by instructor.
Honors Mathematics A
Honors Mathematics A focuses primarily on linear algebra from a rigorous and proof-based perspective.
Typical Topics Using Apostol
- Linear spaces
- Linear transformations and matrices
- Determinants
- Eigenvalues and eigenvectors
- Eigenvalues of operators acting on Euclidean spaces
Typical Topics Using Friedman’s Notes
- Vectors
- Further topics in vectors
- Linear maps
- Row reduction
- Inner products and orthogonality
- Determinants
Honors Mathematics B
Honors Mathematics B continues the sequence with multivariable calculus and related topics developed from a rigorous theoretical perspective.
Typical Topics Using Apostol
- Differential calculus of scalar and vector fields
- Applications of differential calculus, including Lagrange multipliers
- Line integrals
- Multiple integrals
- Surface integrals
Typical Topics Using Friedman’s Notes
- Basic topology of Rn
- Derivatives
- Inverse and implicit function theorems
- Integration
- Integration on manifolds
Course Structure
The sequence includes lectures and mandatory recitation sections. Recitations provide additional opportunities to work through proofs, solve problems, discuss course material, and develop the mathematical writing skills expected in the sequence. Specific assignments, pacing, topic order, and the balance between theory and applications may vary by instructor.
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