Jeremy Sylvestre, PhD, MSc, BSc (Eng)
PhD, Mathematics (Toronto)
MSc, Mathematics (Toronto)
BSc (Eng), Mathematics and Engineering (Queen's)
See contact details above. Email is preferred over voicemail.
If you are a past student and need a syllabus from a past course, please contact the Augustana departmental administrative support staff at firstname.lastname@example.org.
My current research involves developing foundational libraries for the formalization of mathematics.
I teach a variety of introductory 1st- and 2nd-year mathematics courses at the Augustana Campus: calculus, linear algebra, discrete math, and geometry.
Foundational topic of calculus (including differentiation and integration of algebraic, trigonometric, exponential and logarithmic functions; Fundamental Theorem) with a focus on modelling and elementary differential equations. Prerequisite: Mathematics 30-1. Note: Credit may be obtained for only one of AUMAT 116 or 110.
Vector and matrix algebra, determinants, linear systems of equations, vector spaces, eigenvalues and eigenvectors, applications. Prerequisite: Mathematics 30-1.
Further foundational topics in calculus, including: limits of sequences and functions, infinite series (including Taylor and Fourier series) and multi-variable differential calculus. Prerequisites AUMAT 110 or 116, and AUMAT 120.
Groups as a measure of symmetry. Groups of rigid motions. Frieze groups, and finite groups in two and three dimensions. Groups of matrices. Group actions with application to counting problems. Permutation groups. Subgroups, cosets, and Lagrange's Theorem. Quotient groups and homomorphisms. Prerequisites: AUMAT 120 and one of 110 or 116.
Sets, functions, elementary propositional and predicate logic, Boolean algebra, elementary graph theory, proof techniques (including induction and contradiction), and combinatorics. Prerequisites: AUMAT 110 or 116, and 120.
Computational problems in linear algebra, including linear systems and least squares and eigenvalues problems, with matrix factorizations as a main tool for tackling these problems. Prerequisites: AUMAT 240 or AUSCI 250 (2023).