**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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