Calendar#
I will put all deadlines on the Blackboard Calendar. Please check it regularly.
Key university dates#
For official University dates, see the Fall 2026 academic calendar and the Registrar’s final-exam schedule.
| Date | Event |
|---|---|
| Monday, August 17 | Classes begin |
| Monday, September 7 | Labor Day holiday |
| Tuesday, November 24–Friday, November 27 | Thanksgiving holiday |
| Wednesday, December 9 | Final exam: |
Exams#
Daily lecture log#
The public daily log below contains the lectures currently released. Later planning entries remain in the instructor’s private lecture log and do not appear in this navigation.
| Wk | Lec | Topics | Ref |
|---|---|---|---|
| 1 | 2026-08-17 | Sets, cardinality, Cartesian products, and the sum rule. | Set notation and basic counting: from “Set notation” through “The sum rule.” |
2026-08-19 | Product rule; strings with and without repetition. | Set notation and basic counting: sections “The product rule” and “Strings: an important type of counting problems.” | |
2026-08-21 | Subtraction, division, permutations, combinations, and counting models. | More counting techniques: sections “The difference rule,” “The division principle and permutations,” “Unordered selections: combinations without repetition,” and “Counting problems.” | |
| 2 | 2026-08-24 | Lattice paths. Repeated-letter anagrams and multinomial coefficients. Combinations with repetition; stars and bars. | Applications of combinations and combinations with repetition: sections “Lattice paths in the plane,” “Three-dimensional paths and multinomial coefficients,” “Anagrams with repeated letters,” and “Combinations with repetition.” |
2026-08-26 | Choosing the correct model: does order matter and are repetitions allowed. A second bijection for combinations with repetition: increasing integers. Integer solutions with lower bounds. The binomial formulas for | Binomial expansions, Pascal paths, and Catalan numbers: sections “A bakery problem: four kinds of choice,” “Combinations with repetition and cumulative totals,” “Solutions with lower bounds,” and “The binomial theorem.” | |
2026-08-28 | Multinomial formula and polynomial expansions Coefficient extraction from powers of multivariate polynomials. Pascal’s recurrence and triangle: algebraic and combinatorial interpretation. Recursive path counts; paths through or avoiding a specified point; recursive definition; subtraction arguments. | Binomial expansions, Pascal paths, and Catalan numbers: sections “The multinomial theorem,” “Pascal’s recurrence and Pascal’s triangle,” and “Recursive lattice-path counts.” | |
| 3 | 2026-08-31 | Reflection argument and Catalan numbers. Inclusion–exclusion for two, three, and finitely many sets. | Binomial expansions, Pascal paths, and Catalan numbers: section “Catalan paths and the reflection principle.” Inclusion–exclusion and applications: from “The geometry of overlapping sets” through “Proof via indicator functions.” |
2026-09-02 | Characteristic functions. Conclusion of the proof of the inclusion–exclusion principle. Complement and violation-set formulations. | Inclusion–exclusion and applications: sections “Proof via indicator functions” and “The complement and violation-set form.” | |
2026-09-04 | Applications to bounded integer solutions and strings without repeated letters that avoid or contain specified substrings. Euler’s totient function. | Inclusion–exclusion and applications: sections “Integer solutions with upper bounds,” “Strings with forbidden substrings,” and “Euler’s totient function.” | |
| 4 | 2026-09-09 | Review of counting strings that avoid specified substrings. The inclusion–exclusion formula when an intersection size depends only on the number of conditions imposed. Derangements. | Inclusion–exclusion and applications: sections “Strings with forbidden substrings,” “When only the number of imposed conditions matters,” and “Derangements and fixed points.” |
2026-09-11 | Strings that use every symbol, surjective functions, and Stirling numbers. Graphs without isolated vertices. | Inclusion–exclusion and applications: sections “Euler’s totient function,” “Graphs with no isolated vertices,” “Counting surjective functions and full-alphabet strings,” and “Connection with Stirling numbers.” | |
| 5 | 2026-09-14 | Review of rook numbers and rook polynomials, including examples of their computation and use. Introduction to ordinary generating functions: a generating function | Rook polynomials and forbidden positions: all sections. Ordinary generating functions: definitions and series multiplication: all sections. |
2026-09-18 | Midterm 1. | ||
| 6 | 2026-09-21 | Ordinary generating functions; encoding finite and unlimited selections; substitution to track total value; formal power-series multiplication and the Cauchy product; generating-function models for selections with conditions. | Ordinary generating functions: definitions and series multiplication: all sections. |
2026-09-23 | Infinite formal power series and rational functions; constrained integer equations; combinatorial interpretations of powers and products; operations on generating functions; application to the sum of squares. | Ordinary generating functions: advanced techniques: all sections except coefficient extraction. | |
2026-09-25 | |||
| 7 | 2026-09-28 | ||
2026-09-30 | |||
2026-10-02 | Introduction to solving homogeneous linear recurrences with constant coefficients: classification of recurrences and the first steps toward closed formulas. | Solving linear recurrences with constant coefficients: sections “Review: classifying recurrence relations” and “Homogeneous recurrences with real characteristic roots” (subsection “Distinct real roots and the opening problem”). | |
| 8 | 2026-10-05 | No class. | |
2026-10-07 | The characteristic polynomial of a linear recurrence with constant coefficients. Solutions of homogeneous recurrences; roots with multiplicity. Nonhomogeneous recurrences: particular solutions and the general solution. | Solving linear recurrences with constant coefficients: sections “Homogeneous recurrences with real characteristic roots” (subsections “Repeated real roots and the shift operator” and “Summary of the homogeneous solution procedure”) and “Nonhomogeneous polynomial–exponential driving terms.” | |
2026-10-09 | |||
| 9 | 2026-10-12 | ||
2026-10-14 | From a transition-matrix (vector) recurrence to a scalar recurrence relation. Computing terms of a recurrence with a logarithmic number of matrix multiplications. | Finite state machines and vector recurrences: sections “From a vector recurrence to a scalar recurrence” and “Computing matrix powers.” | |
2026-10-16 | Midterm 2. | ||
| 10 | 2026-10-19 | No class. | |
2026-10-21 | Colorings of the corners of a square up to rotation, and the definition of a group. Dihedral groups: the symmetries of a regular polygon, the rotation | Groups: sections “Coloring the corners of a square,” “Groups,” “The symmetries of a regular polygon,” “Presentations,” “The symmetric group,” and “Cycle notation.” |
Week and unit overview#
| Weeks | Unit | Topic |
|---|---|---|
| 1–4 | Unit I: Enumeration | Counting models, bijections, double counting, and inclusion-exclusion |
| 4–5 | Unit II: Generating-function foundations | Formal power series and ordinary generating-function operations |
| 6–8 | Unit III: Recurrences | State models, linear recurrences, recursive evaluation, and dynamic programming |
| 9–16 | Further topics | To be announced |