Teaching
Concordia University
Jan.-Apr., 2026 - MATH 205 /4 H Differential and Integral Calculus II
Textbook: Thomas' Calculus: Early Transcendentals, Single Variable.
Other suggested references:
1) APEX Math 2560: Calculus II (University of Lethbridge)
2) APEX Math 2570: Calculus III - Sequences and Series (University of Lethbridge)
3) Paul's Online Notes - Calculus II (Lamar University)
Course Content:
Week 1
5.1 Area and Estimating with Finite Sums
5.2 Sigma Notation and Limits of Finite Sum
5.3 The Definite Integral
Week 2
4.8 Antiderivatives
5.4 The Fundamental Theorem of Calculus
Week 3
5.5 Indefinite Integrals and the Substitution Method
5.6 Definite Integral Substitutions, Area Between Curves
Week 4
8.1 Using Basic Integration Formulas
8.2 Integration by Parts
Week 5
8.3 Trigonometric Integrals
8.4 Trigonometric Substitution
Week 6
8.5 Integration of Rational Functions by Partial Fractions
6.1 Volumes Using Cross-Sections (emphasis on the disk/washer method)
Week 7
8.8 Improper Integrals
Week 8
10.1 Sequences
10.2 Infinite Series
Week 9
10.3 The Integral Test
10.4 The Comparison Tests
Week 10
10.5 Absolute Convergence, Ratio and Root Tests
10.6 Alternating Series and Conditional Convergence
Week 11
Power Series (omit Multiplication of Series)
10.8 Taylor and Maclaurin series
Université du Luxembourg
Mar.-Jun., 2024 - Algebraic Number Theory (Master level course)
Textbook: Algebraic Number Theory by J.S. Milne
The month of March was taught by Antonella Perucca.
Sep. 11 and 13, 2024 - Linear Algebra preparatory course instructor at the Prep Camp Mathematics 2024 (in French)
Sep. 2024 - Jan., 2025 - Commutative Algebra (Master level course) - Problem Sessions Instructor
Textbook: Private course notes by Gabor Wiese
Feb.-Jun., 2025 - Algebraic Number Theory (Master level course)
Textbook: Private course notes by myself
Course Description:
Review of integrality and Dedekind domains, including the factorisation of prime ideals. Proof that the ring of integers of a number field is a Dedekind domain. Study of some properties of the ring F_q[t],
Valuations, places, rational function fields.
Zeta functions of F_q[t], Q and F_q(t) and some arithmetic consequences of their properties,
Gauss reciprocity over number fields and global function fields and related subjects,
Extensions of Dedekind domains and their fraction fields,
Decomposition groups, inertia groups and basic properties,
Cyclic extensions over number fields and global function fields,
Dirichlet L-series and primes in arithmetic progressions,
Study of rings of integers I: Minkowski Theory and Class Number,
Study of rings of integers II: Dirichlet’s Unit Theorem,
Time permitting: An introduction to Drinfeld modules
University of Lethbridge
Sep.-Dec., 2022 - Math 1560 - Section A : Calculus I
Textbook: APEX Calculus
May-Jun., 2023 - Math 1560 - Section A : Calculus I
Textbook: APEX Calculus
Sep.-Dec., 2023 - MATH 3410A - Linear Algebra
Textbook: Private Notes inspired by Algebra, 2nd edition by Michael Artin, Chapters 1, 3, 4 and 8
Supervision
Undergraduate Students
Supervision type: Bachelor Seminar Project
Student Name: Victor Souirji
Program, year: Bachelor in Mathematics, 1st year, second semester
Supervision dates: Co-supervision with Antonella Perucca from February to June 2025
Location: University of Luxembourg
Brief description of student's output: The resulting work consisted of a slide presentation that the student used to present his work at an undergraduate seminar.
Supervision type: Bachelor Thesis
Student Name: Ben Welter
Program, year: Bachelor in Mathematics, 4th (and final) year
Supervision dates: February to June 2025
Location: University of Luxembourg
Brief description of student's output: Bachelor thesis explaining details from Schoof's algorithm's original paper.
Open Access: Available on the University of Luxembourg Open repository and Bibliography website (ORBilu).
Graduate Students
Supervision type: Master in Mathematics Semester Project
Student Name: Dewei (Dave) Zou
Program, year: Master in Mathematics, first year
Supervision dates: September to December 2024
Location: University of Luxembourg
Brief description of student's output: A 60 pages pdf document written by the student on learning foundational concepts of modern algebraic geometry developed by Alexander Grothendieck. This represents work of at least 100 hours.