DENIF – Documents d’Enseignement Numériques en Informatique Fondamentale

   Course Slides  

•   Good and Bad Proofs
•   Propositions and Proofs
•   Proofs by Contradiction and Cases
•   Predicate Logic
•   Sets and Functions
•   Induction I
•   Induction II
•   Relations I
•   Relations II
•   Graph Theory I
•   Graph Theory II
•   Graph Theory III
•   Graph Theory IV
•   Graph Theory IV (cont.)
•   Number Theory I and II
•   Number Theory III
•   State Machines I: Invariants / Fallacies with Infinity
•   State Machines II: Derived Variables, Stable Marriage Problem
•   Sums and Series I
•   Sums and Series II
•   Asymptotics
•   Law of Large Numbers
•   Random Walks

   In-Class Problems  

•   Good and Bad Proofs - Course Information
•   Good and Bad Proofs - Course Information - solutions
•   Propositions and Proofs
•   Propositions and Proofs - solutions
•   Proofs by Contradiction and Cases
•   Proofs by Contradiction and Cases - solutions
•   Predicate Logic
•   Predicate Logic - solutions
•   Sets and Functions
•   Sets and Functions - solutions
•   Induction I
•   Induction I - solutions
•   Induction II
•   Induction II - solutions
•   Relations I
•   Relations I - solutions
•   Relations II
•   Relations II - solutions
•   Graph Theory I
•   Graph Theory I - solutions
•   Graph Theory II
•   Graph Theory II - solutions
•   Graph Theory III
•   Graph Theory III - solutions
•   Graph Theory IV
•   Graph Theory IV - solutions
•   Number Theory I
•   Number Theory I - solutions
•   Number Theory II
•   Number Theory II - solutions
•   Number Theory III
•   Number Theory III - solutions
•   State Machines I: Invariants Fallacies with Infinity
•   State Machines I: Invariants Fallacies with Infinity - solutions
•   State Machines II: Derived Variables, Stable Marriage Problem
•   State Machines II: Derived Variables, Stable Marriage Problem - solutions
•   Sums and Series I
•   Sums and Series I - solutions
•   Sums and Series II
•   Sums and Series II - solutions
•   Asymptotics
•   Asymptotics - solutions
•   Counting I
•   Counting I - solutions
•   Counting II
•   Counting II - solutions
•   Counting III (with Magic Trick Solution)
•   Counting III (with Magic Trick Solution) - solutions
•   Counting IV
•   Counting IV - solutions
•   Generating Functions I
•   Generating Functions I - solutions
•   Generating Functions II
•   Generating Functions II - solutions
•   Introduction to Probability
•   Introduction to Probability - solutions
•   Conditional Probability and Independence
•   Conditional Probability and Independence - solutions
•   Random Variables
•   Random Variables - solutions
•   Distribution and Density, Binomial Distribution
•   Distribution and Density, Binomial Distribution - solutions
•   Expectation
•   Expectation - solutions
•   Linearity of Expectation
•   Linearity of Expectation - solutions
•   Variance
•   Variance - solutions
•   Sampling and Confidence
•   Sampling and Confidence - solutions
•   Law of Large Numbers
•   Law of Large Numbers - solutions
•   Random Walks
•   Random Walks - solutions

   Assignments and Solutions  

•   Propositions and Proofs
•   Propositions and Proofs - solutions
•   Induction I
•   Induction I - solutions
•   Relations I
•   Relations I - solutions
•   Graph Theory II
•   Graph Theory II - solutions
•   Number Theory I
•   Number Theory I - solutions
•   State Machines I : Invariants / Fallacies with Infinity
•   State Machines I : Invariants / Fallacies with Infinity - solutions
•   Counting I
•   Counting I - solutions
•   Generating Functions I
•   Generating Functions I - solutions
•   Introduction to Probability
•   Introduction to Probability - solutions
•   Expectation
•   Expectation - solutions

   Exams and solutions  

•   Practice Quiz 1
•   Practice Quiz 1 - solutions
•   Quiz 1
•   Quiz 1 - solutions
•   Quiz 2
•   Quiz 2 - solutions
•   Final Exam
•   Final Exam - solutions

   Lecture Notes  

•   Logic and Sets
•   Proofs
•   Induction I
•   Induction II
•   Induction III
•   Number Theory I
•   Number Theory II
•   Graphs I
•   Graphs II
•   Summations
•   Approximations, Asymptotics
•   Recurrences
•   Counting I
•   Counting II
•   Counting III
•   Generating Functions
•   Probability
•   Conditional Probability
•   Independence
•   Random Variables and Distributions
•   Expectation I
•   Expectation II
•   Random Walks
•   Special Topics

   Problem Set and Solutions  

•   Set 1
•   Set 2
•   Set 3
•   Set 4
•   Set 5
•   Set 6
•   Set 7
•   Set 8
•   Set 9
•   Set 10
•   Set 11

   Recitations  

•   Logic
•   Case Analysis
•   Induction
•   Strong Induction
•   Well-ordering Principle
•   The Pulverizer
•   RSA
•   Graphs and Trees
•   Bipartite Graphs
•   Sums and Approximations
•   The Quest
•   Solving Linear Recurrences
•   Basic Counting Notions
•   Counting Rules
•   Counting
•   Generating Functions and Expressions
•   The Four-Step Method
•   Law of Total Probability
•   Probability
•   Random Variables, Distributions, etc.
•   Expected Value
•   Conditional and Total Expectation
•   Stencil the Flea

   Lecture Notes  

•   Course Notes 1 - Proofs
•   Course Notes 2 - Induction
•   Course Notes 3 - Relations
•   Course Notes 4 - Graphs
•   Course Notes 5 - State Machines: Invariants and Termination
•   Course Notes 6 - Recursive Definitions and Structural Induction
•   Course Notes 7 - Sums, Products & Asymptotics
•   Course Notes 8 - Basic Counting, Pigeonholing, Permutations
•   Course Notes 9 - Permutations and Combinations
•   Course Notes 10 - Introduction to Probability
•   Course Notes 11-12 - Random Variables and Expectation
•   Course Notes 13-14 - Deviation from the Mean
•   Course Notes 15 - Milestones of Probability Theory

   Course Slides  

•   Lecture Slides 1-1
•   Lecture Slides 1-2
•   Lecture Slides 2-1
•   Lecture Slides 2-2
•   Lecture Slides 2-3
•   Lecture Slides 3-1
•   Lecture Slides 3-2
•   Lecture Slides 3-3
•   Lecture Slides 4-1
•   Lecture Slides 4-2
•   Lecture Slides 5-1
•   Lecture Slides 5-2
•   Lecture Slides 5-3
•   Lecture Slides 6-1
•   Lecture Slides 6-2
•   Lecture Slides 7-1
•   Lecture Slides 7-2
•   Lecture Slides 8-1
•   Lecture Slides 8-2
•   Lecture Slides 8-3
•   Lecture Slides 9-1
•   Lecture Slides 9-2
•   Lecture Slides 9-3
•   Lecture Slides 10-1
•   Lecture Slides 10-2
•   Lecture Slides 10-3
•   Lecture Slides 11-1
•   Lecture Slides 12-1
•   Lecture Slides 12-2
•   Lecture Slides 12-3
•   Lecture Slides 13-1
•   Lecture Slides 13-2
•   Lecture Slides 14-1
•   Lecture Slides 14-2
•   Lecture Slides 14-3
•   Lecture Slides 15-1

   Class Problems and Solutions  

•   Week 1 A
•   Week 1 B
•   Week 2 A
•   Week 2 B
•   Week 3 A
•   Week 3 B
•   Week 4 A
•   Week 4 B
•   Week 5 A
•   Week 5 B
•   Week 6 A
•   Week 6 B
•   Week 7 A
•   Week 7 B
•   Week 8 A
•   Week 8 B
•   Week 8 C
•   Week 9 A
•   Week 9 B
•   Week 9 C
•   Week 10 A
•   Week 10 B
•   Week 10 C
•   Week 11 A
•   Week 12 A
•   Week 12 B
•   Week 12 C
•   Week 13 A
•   Week 13 B
•   Week 14 A
•   Week 14 B
•   Week 14 C
•   Week 15 A

   Assignments and Solutions  

•   Set 1
•   Set 2
•   Set 3
•   Set 4
•   Set 5
•   Set 6-7
•   Set 8
•   Set 9
•   Set 10
•   Set 11-12
•   Set 13-14