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MATH UN1207 Honors Mathematics A (fall only): College Bulletin


MATH UN1208 Honors Mathematics B (spring only): College Bulletin

Prerequisites:  (see Courses for First-Year Students). The second term of this course may not be taken without the first.

This two semester sequence covers multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major.


  • Tom M. Apostol, Calculus, 2nd edition, Volume II (Publisher link)
  • Friedman’s notes for Honors Math (PDF)

Sample Syllabus, Honors Math A: Chapter 1-5 of Apostol’s Volume II or Friedman’s notes for Honors A (Chapter 1-6)


1. Linear Spaces

2. Linear Transformations and matrices

3. Determinants

4. Eigenvalues and Eigenvectors

5. Eigenvalues of operators acting on Euclidean spaces


1. Vectors

2. More Vectors

3. Linear maps

4. Row reduction

5. Inner product and orthogonality

6. Determinants

Sample Syllabus, Honors Math B: Chapter 8-12 of Apostol’s Volume II or Friedman’s notes for Honors B (Chapter 7-11)


8. Differential Calculus of scalar and vector fields

9.  Applications of the differential Calculus (Lagrange’s multipliers)

10. Line integrals

11. Multiple integrals

12. Surface integrals


7. Basic topology of R^n

8. Derivatives

9. Inverse and implicit function theorems

10. Integration

11. Integration on manifolds



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