Jeremy Sylvestre, PhD, MSc, BSc (Eng)
PhD, Mathematics (Toronto)
MSc, Mathematics (Toronto)
BSc (Eng), Mathematics and Engineering (Queen's)
I teach a variety of introductory 1st- and 2nd-year mathematics courses at the Augustana Campus: calculus, linear algebra, discrete math, and geometry.
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If you are a past student and need a syllabus from a past course, please contact the Augustana departmental administrative support staff at email@example.com.
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.
Vector spaces, bases, linear transformations, change of bases, eigenvectors, characteristic polynomials, diagonalization, inner products and Gram-Schmidt orthogonalization, orthogonal and unitary operators. Prerequisites: AUMAT 120 and one of 110 or 116.
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.
Intensive study of a specific problem or area of mathematics as defined by the student and a supervising instructor. Prerequisite: Fourth-year standing. Notes: Admission to AUMAT 495 normally requires a minimum GPA of 3.0 on the major in Mathematics and Physics. An Application for Individual Study must be completed and approved before registration in the course.