# Honors Courses

*Honors Mathematics Course Descriptions*

A typical sequence of courses taken by honors students can be found in the advising handbook (pages 13--14). Here is a detailed description of each of the honors courses.

### Calculus sequence

**MATH 10850 (Honors Calculus I)** (offered every fall)

Official course description: A rigorous course in differential and integral calculus of one variable. Topics include an axiomatic formulation of the real numbers, mathematical induction, infima and suprema, functions, continuity, derivatives, integrals, infinite sequences and series, transcendental functions and their inverses, and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. NB: this course should not be confused with MATH 10450, Honors Mathematics I, which is associated with the Glynn Family Honors Program.

**MATH 10860 (Honors Calculus II)** (offered every spring)

Official course description: A rigorous course in differential and integral calculus of one variable. Topics include an axiomatic formulation of the real numbers, mathematical induction, infima and suprema, functions, continuity, derivatives, integrals, infinite sequences and series, transcendental functions and their inverses, and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject. NB: this course should not be confused with MATH 10460, Honors Mathematics II, which is associated with the Glynn Family Honors Program.

**MATH 20850 (Honors Calculus III)** (offered every fall)

Official course description: A rigorous course in differential and integral calculus of several variables. Topics include functions of several variables, the inverse function theorem, partial derivatives, multiple integrals, line integrals, surface integrals, Stokes' theorem, an introduction to ordinary differential equations and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject.

**MATH 20860 (Honors Calculus IV)** (offered every spring)

Official course description: A rigorous course in differential and integral calculus of several variables. Topics include functions of several variables, the inverse function theorem, partial derivatives, multiple integrals, line integrals, surface integrals, Stokes' theorem, an introduction to ordinary differential equations and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject.

### Algebra sequence

**MATH 20810 (Honors Algebra I)** (offered every fall)

Official course description: A comprehensive treatment of vector spaces, linear transformations, inner products, determinants, eigenvalues, tensor and exterior algebras, spectral decompositions of finite-dimensional symmetric operators, and canonical forms of matrices. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject.

**MATH 20820 (Honors Algebra II)** (offered every spring)

Official course description: A comprehensive treatment of vector spaces, linear transformations, inner products, determinants, eigenvalues, tensor and exterior algebras, spectral decompositions of finite-dimensional symmetric operators, and canonical forms of matrices. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject.

**MATH 30810 (Honors Algebra III)** (offered every fall)

Official course description: A comprehensive treatment of groups, polynomials, rings, homomorphisms, isomorphism theorems, field theory, and Galois theory. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject.

**MATH 30820 (Honors Algebra IV)** (offered every spring)

Official course description: A comprehensive treatment of groups, polynomials, rings, homomorphisms, isomorphism theorems, field theory, and Galois theory. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject.

### Analysis sequence

**MATH 30850 (Honors Analysis I)** (offered every fall)

Official course description: An advanced course in mathematical analysis in one and several variables. Topics include an axiomatic formulation of the real and complex number systems, compactness, connectedness, metric spaces, limits, continuity, infinite sequences and series, differentiation, the Riemann-Stieltjes integral, the Stone-Weierstrass theorem, the implicit function theorem, differential forms, partitions of unity, simplexes and chains, and Stokes' theorem.

**MATH 30860 (Honors Analysis II) **(offered every spring)

Official course description: An advanced course in mathematical analysis in one and several variables. Topics include an axiomatic formulation of the real and complex number systems, compactness, connectedness, metric spaces, limits, continuity, infinite sequences and series, differentiation, the Riemann-Stieltjes integral, the Stone-Weierstrass theorem, the implicit function theorem, differential forms, partitions of unity, simplexes and chains, and Stokes' theorem.