Discrete Mathematics and Calculus
(VU Amsterdam, Computer Science students, Second Semester 2025-2026)
Due to the disruption affecting Canvas at VU Amsterdam, I am sharing the main course information here.
If needed, announcements will be made in class and shared on this page in case Canvas is not working.
The course schedule remains available on Rooster.
Textbooks
For Lectures 1−7 (Discrete Mathematics):
For Lectures 8−12 (Calculus):
Robert A. Adams and Christopher Essex, Calculus: A Complete Course, 10th edition.
You may also be able to follow the second part of the course using the 9th edition or earlier, but please note that in this case, the numbering of sections and exercises may differ.
Prerequisites
The first part of the course (Discrete Mathematics) builds upon some of the concepts introduced in the "Logic and Sets" course. In particular, familiarity with proof by induction is particularly important, as it will play a key role in solving problems and understanding the material in this part.
The second part of the course (Calculus) builds upon the foundational mathematics that is typically taught in high school programs around the world. As such, some prerequisites will be assumed, most of which can be found in the Preliminaries chapter of the Calculus textbook.
Exam dates
Final exam: May 27, 2026
Resit exam: July 3, 2026
Lecture 1
For this lecture, we are using the Discrete Mathematics book.
Theory:
§2.1: Some essential problems in combinatorics
§2.2 (until page 140): Binomial Coefficients
Exercises (for the tutorials):
§2.1: 2
§2.2: 2, 10
Lecture 2
For this lecture, we are using the Discrete Mathematics book.
Theory:
§2.3: Multinomial Coefficients
§2.4: The Pigeonhole Principle
Exercises (for the tutorials):
§2.3: 1, 2, 5
§2.4: 1, 8
Lecture 3
For this lecture, we are using the Discrete Mathematics book.
Theory:
§1.1: Introductory concepts in graph theory
Exercises (for the tutorials):
§1.1.2: 1, 2, 3
§1.1.3: 2, 3, 7, 10
Lecture 4
For this lecture, we are using the Discrete Mathematics book.
Theory:
§1.2: Distance in graphs
§1.3.1: Trees - Definitions and examples
§1.3.2: Properties of Trees
§1.3.3: Spanning Trees
Exercises (for the tutorials):
§1.2.2: 2, 4
§1.3.1: 4
§1.3.2: 2, 5
§1.3.3: 5
Lecture 5
For this lecture, we are using the Discrete Mathematics book.
Theory:
§1.4.1: The Bridges of Königsberg
§1.4.2: Eulerian Trails and Circuits
§1.4.3 (until page 63): Hamiltonian Paths and Cycles
Exercises (for the tutorials):
§1.4.2: 1, 4
§1.4.3: 4, 10
Lecture 6
For this lecture, we are using the Discrete Mathematics book.
Theory:
§1.5.1: Planarity - Definitions and examples
§1.5.2: Euler's Formula
§1.5.4: Kuratowski's Theorem
§1.6.1: Colorings - Definitions
§1.6.3: The Four Color Problem
§1.6.2: Bounds on Chromatic Number
Exercises (for the tutorials):
§1.5.1: 8
§1.5.2: 1, 2, 6
§1.5.4: 2, 4
Lecture 7
Theory:
General remarks on directed graphs. This material is not covered in the book, but all necessary concepts are provided in the slides.
Exercises (for the tutorials):
§1.6.1: 1, 4, 5
§1.6.2: 5
Lecture 8
For this lecture, we are using the Calculus book.
Theory:
§P.1: Notation: sets, numbers, intervals
§P.4, P.5: Functions: domain, codomain, range, composition
§1.2: Limits
§1.3: Limits at infinity and infinite limits
Exercises (for the tutorials):
§P.4: 5, 7
§P.5: 1, 7, 25
§1.2: 7, 13, 15, 21, 25, 29, 51, 59, 61, 63, 65
§1.3: 3, 7, 9, 23, 29
Lecture 9
For this lecture, we are using the Calculus book.
Theory:
§1.4: Continuity
§2.2: The derivative and differentiability
§2.3, §2.4: Differentiation rules
§2.6: Higher-order derivatives
Exercises (for the tutorials):
§1.4: 1, 7, 9, 15
§2.2: 15, 25, 27
§2.3: 33, 35
§2.4: 3, 13, 15
§2.5: 5, 17, 31
§2.6: 5, 9, 11, 25
Lecture 10
For this lecture, we are using the Calculus book.
Theory:
§3.1: Inverse functions
§3.2: Exponential and logarithmic functions and identities
§3.3: Logarithmic differentiation
§3.4: Limits involving logarithms and exponentials
§4.3: L'Hôpital's rule
Exercises (for the tutorials):
§3.1: 11, 23
§3.2: 3, 9, 15, 33
§3.3: 9, 17, 49
§3.4: 3, 7
§4.3: 3, 13, 23
Lecture 11
For this lecture, we are using the Calculus book.
Theory:
§4.4: Extreme values
§4.5: Concavity and inflections
§4.6: Sketching graphs
§4.10: Taylor polynomials
Exercises (for the tutorials):
§4.4: 3, 13, 25, 35
§4.5: 7
§4.6: 15, 33, 39
§4.10: 3, 7, 11
Lecture 12
For this lecture, we are using the Calculus book.
Theory:
§2.10, §5.3: Definitions of integral and integrable functions
§5.4: Properties of the definite integral
§5.5: The Fundamental Theorem of Calculus
§5.6: Method of substitution
§6.1: Integration by parts
§13.1, §13.3: Definition of partial derivatives
Exercises (for the tutorials):
§2.10: 3, 9, 14
§5.4: 9, 13, 19
§5.5: 3, 5, 9, 17, 21, 23
§5.6: 3, 21
§6.1: 1, 17
§13.3: 1, 3, 7