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Honors Math

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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