Teaching Schedule

Fall 2019: On Sabbatical Leave.

Spring 2020:

Mat 330, Linear Algebra. "Introduction to linear algebra, including matrices and linear transformations, eigenvalues, and eigenvectors." Prerequisite, M182. 3 credits.
- Textbook: Howard Anton, Elementary Linear Algebra. Officially(?), we will use the 12e (which has a second author, Anton Kaul), but the 10th edition should work fine. (The 11th edition should work fine too, but I don't have a copy, so I would prefer you find the 10th edition, if you choose this economical route.)

Summer 2020 (Session 3, July 13 -- August 14):

MAT 283, Intermediate Calculus. "Vectors; differentiation and integration of vector valued functions; multivariable calculus; partial derivatives; multiple integrals and applications; line, surface, and volume integrals; Green's theorem; divergence theorem; and Stoke's theorem." Prerequisites: MAT 182. 4 credits.
College Geometry, MATH 480/680. "Study of advanced geometrical topics using the methods of proof of elementary geometry." Prerequisite: MAT 181 or consent of the instructor. 3 credits.
- Textbook: Baragar, A survey of classical and modern geometries. This book is out of print. I will probably have reprographics produce a course packet.

Archives:

MAT 126, Precalculus I. Fall 2007. "Topics include fundamentals of algebra, functions and graphs, polynomial, rational, exponential, and logarithmic functions, and systems of linear equations." 3 credits.
MAT 127, Precalculus II. Fall, 2003. "Topics include circular functions, trigonometric identities and equations, conic sections, complex numbers, and discrete algebra." Prerequisite: MAT 126, a score of 24 on the ACT, or a score of 560 on the SAT. 3 credits.
MAT 181, Elementary Calculus I, Fall, 2002, Fall 2004, Summer 2009, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 201. "Differentiation and integration of algebraic and transcendental functions, with applications." Prerequisite: MAT 128 or equivalent. 4 credits.
MAT 182, Elementary Calculus II, Spring 2003, Fall 2009, Fall 2010, Fall 2011, Fall 2013, Summer 2018, Summer 2019. "Further applications and techniques of integration including integration by parts, sequences and series, polynomial approximations." Prerequisite: MAT 181. 4 credits.
Math 250x (Spring 2015, cancelled), Experimental Milestone Course in the Department of Mathematical Sciences. The aim of this course is to inform and excite majors in the Mathematical Sciences about their future courses in mathematics and in mathematics in general. 2 credits.
MATH 251, Discrete Mathematics I, Spring 2007. "Topics include set operations, Cartesian product relations and functions, equivalence relation, graphs and digraphs, propositional calculus, truth tables, mathematical induction, elementary combinatorics with applications to probability." Corequisite: MATH 182. 3 credits.
MAT 283, Intermediate Calculus, Spring, 2002, Fall 2005, Spring 2018. "Vectors; differentiation and integration of vector valued functions; multivariable calculus; partial derivatives; multiple integrals and applications; line, surface, and volume integrals; Green's theorem; divergence theorem; and Stoke's theorem." Prerequisites: MAT 182. 4 credits.
Mat 330(formerly MAT 253), Linear Algebra, Spring 2002, Fall 2006, Summer 2010, Fall 2017. "Introduction to linear algebra, including matrices and linear transformations, eigenvalues, and eigenvectors." Prerequisite, M182. 3 credits.
MAT 351, Discrete Mathematics II, Spring 2003, Spring 2004, Spring 2005, Spring 2012, Fall 2012, Spring 2014. "Infinite sets, Cantor's diagonal argument, first order logic, formal and informal proofs, combinatorics, Boolean algebra, lattices and graphs." Prerequisites: MAT 182. The course has change, but for some reason, the description has not. A more accurate description would be "Modular arithmetic and number theory, leading up to RSA (the first public key code system), and graph theory (leading up to the five color theorem)."
MATH 427, Differential Equations I, "[Together with MATH 428] Theory and solution techniques for solving ordinary differential equations with constant and variable coefficients, systems of linear differential equations, Laplace transform, difference equations and numerical methods. Fourier Series; stability theory and autonomous systems." Prerequisites: MATH 283; Math 330 or Math 365. 3 credits.
MATH 453/653, Abstract Algebra I. Fall 2008, Fall 2009, Fall 2015, Fall 2016, Fall 2018. "[Together with MATH 454, topics include] sets, functions, groups, quotient groups, homomorphism theorems, Abelian groups, rings, polynomial rings, division rings, Euclidean domains, fields and vector spaces." Prerequisites: MATH 251 and MATH 330. 3 credits.
MATH 454/654, Abstract Algebra II, Spring 2009, Spring 2010, Spring 2016, Spring 2017. Spring 2019."[Together with MATH 453, topics include] sets, functions, groups, quotient groups, homomorphism theorems, Abelian groups, rings, polynomial rings, division rings, Euclidean domains, fields and vector spaces." Prerequisites: MATH 453. 3 credits.
MAT 455, Number Theory I, Fall 2007, Fall 2008. "Topics [together with MATH 456] include divisibility, arithmetic functions, congruences, quadratic residues, primitive roots, Diophantine equations, continued fractions, algebraic numbers, partitions." Prerequisite: MATH 330. 3 credits.
MATH 456/656, Number Theory II, Spring 2008. "Topics [together with MATH 455] include divisibility, arithmetic functions, congruences, quadratic residues, primitive roots, Diophantine equations, continued fractions, algebraic numbers, partitions." Prerequisite: MATH 455. 3 credits.
MAT 480, College Geometry, Fall, 2002, Fall, 2003, Spring 2003, Fall 2004, Spring 2005, Fall 2005, Fall 2006, Spring 2007, Fall 2007, Spring 2008, Spring 2009. Spring 2010, Summer 2010, Spring 2011, Spring 2012 Summer 2012,Spring 2013, Summer 2013, Spring 2014, Spring 2015, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019. "Study of advanced geometrical topics using the methods of proof of elementary geometry." Prerequisite: MAT 181 or consent of the instructor. 3 credits.
MATH 703, Abstract Algebra III, Fall 2010, Fall 2012, Fall 2014. " Detailed study of the following algebraic structures: groups, rings and ideals, fields, modules, and Galois theory." Prerequisite: A year of undergraduate abstract algebra or consent of instructor. 3 credits.
MATH 704, Abstract Algebra IV, Spring 2011, Spring 2013, Spring 2015. "Detailed study of the following algebraic structures: groups, rings and ideals, fields, modules, and Galois theory." Prerequisite: MATH 703 or consent of instructor. 3 credits.
MATH 756, Arithmetic on Elliptic Curves, Fall 2013. "The group structure of elliptic curves over the reals, complex numbers, the rationals, number fields, and finite fields; Bezout's theorem and its applications; projective geometry; genus; Mordell's theorem; points of finite order; and heights. Additional topics may include complex multiplication; modular forms; and factoring using elliptic curves." Prerequisites: MATH 653 and 654, or equivalent. 3 credits.
MAT 789, Elliptic curves (Advanced Topics in Mathematics). Cancelled, Fall, 2003. In this course, we will study elliptic curves, a topic in number theory and algebraic geometry. The subject is both old and ubiquitous. Certain properties of elliptic curves were known to Fermat. Euler used elliptic curves to prove Fermat's Last Theorem for n = 3. Modern research on elliptic curves was instrumental in Andrew Wiles' proof of Fermat's Last Theorem. The theory of elliptic curves also has remarkable relevance to our modern society. There are elliptic curve based cryptographic schemes, and there is an elliptic curve algorithm for factoring large numbers (the latter is useful for breaking certain codes). We will only touch on some of these topics. Prerequisites: Abstract Algebra (MAT 453/653 and 454/654), or consent of the instructor. 3 credits. If you are interested in taking this course, please let me know. Thank you.
MATH 789, Topics in Advanced Mathematics (Advanced geometry). 3 credits