MATH UN1207 Honors Mathematics A (fall only): College Bulletin
and
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.
Textbooks:
- Tom M. Apostol, Calculus, 2nd edition, Volume II (Publisher link)
OR - 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)
Apostol:
1. Linear Spaces
2. Linear Transformations and matrices
3. Determinants
4. Eigenvalues and Eigenvectors
5. Eigenvalues of operators acting on Euclidean spaces
Friedman:
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)
Apostol:
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
Friedman:
7. Basic topology of R^n
8. Derivatives
9. Inverse and implicit function theorems
10. Integration
11. Integration on manifolds
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