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Course Content
Module 1
0/89
Topic 1: The Foundations: Logic and Proofs
02:53
LO1: Understand and Apply Propositional Logic, including Truth Tables
20:46
LO2: Discuss Logical Equivalences and Quantifiers
23:37
LO3: Analyze and construct Valid Arguments using Rules of Inference
18:54
LO4: Differentiate between Direct, Indirect, and Proof by Contradiction Techniques
13:41
LO5: Knowledge Check
15:00
Case Study: The Foundations: Logic and Proofs
15:00
Topic 2: Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
03:36
LO1: Define and perform Operations on Sets
08:13
LO2: Understand the concept of Functions
11:51
LO3: Analyze Sequences and their properties
08:49
LO4: Apply Summation Notation and Compute Sums using Formulas
11:43
LO5: Understand the Basics of Matrices, including Matrix Operations and Determinants
10:10
LO6: Knowledge Check
15:00
Case Study: Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
15:00
Topic 3: Algorithms
03:12
LO1: Understand the concept of Algorithms and their Role in Problem-Solving
15:07
LO2: Analyze the efficiency of Algorithms using Notations
07:55
LO3: Explore various Algorithmic Paradigms
08:02
LO4: Elaborate common Algorithms for Sorting, Searching, and Graph Traversal
24:12
LO5: Knowledge Check
15:00
Case Study: Algorithms
15:00
Topic 4: Number Theory and Cryptography
02:25
LO1: Understand the Basic Principles of Number Theory
11:45
LO2: Apply the Euclidean Algorithm and Modular Arithmetic in Problem-Solving
09:31
LO3: Explore Concepts of Cryptography
11:46
LO4: Knowledge Check
15:00
Case Study: Number Theory and Cryptography
15:00
Topic 5: Induction and Recursion
02:40
LO1: Discuss and apply the Principle of Mathematical Induction
08:13
LO2: Understand and apply Strong Induction in more Complex Proofs
06:39
LO3: Explore the concept of Recursion and its Relation to Inductive Reasoning
08:25
LO4: Knowledge Check
15:00
Case Study: Induction and Recursion
15:00
Topic 6: Counting
03:02
LO1: Understand the Basic Principles of Counting
12:19
LO2: Explore Permutations and Combinations and their Applications
11:38
LO3: Apply the Binomial Theorem in Solving Counting Problems
06:35
LO4: Understand and Solve problems Using the Pigeonhole Principle
06:22
LO5: Knowledge Check
15:00
Case Study: Counting
15:00
Topic 7: Discrete Probability
03:02
LO1: Understand the Basic Principles of Probability
15:33
LO2: Calculate Probabilities using Conditional Probability and Independence
15:45
LO3: Apply Bayes’ Theorem in Problem-Solving
14:30
LO4: Explore Discrete Random Variables and their Expected values
11:01
LO5: Knowledge Check
15:00
Case Study: Discrete Probability
15:00
Topic 8: Advanced Counting Techniques
03:01
LO1: Discuss Advanced Counting Techniques
07:26
LO2: Understand and Apply Recurrence Relations in Solving Counting Problems
13:59
LO3: Analyze Problems using the Principle of Inclusion-Exclusion
10:31
LO4: Solve Complex Counting Problems using Generating Functions
06:20
LO5: Knowledge Check
15:00
Case Study: Advanced Counting Techniques
15:00
Topic 9: Relations
02:50
LO1: Discuss Relations and their Properties
09:05
LO2: Analyze Equivalence Relations and Partitions
10:01
LO3: Explore Partial Orderings and their Applications
07:08
LO4: Understand and Construct Hasse Diagrams
11:38
LO5: Knowledge Check
15:00
Case Study: Relations
15:00
Topic 10: Graphs
02:49
LO1: Understand the fundamental concepts of Graph Theory
10:58
LO2: Analyze Graph Connectivity
08:47
LO3: Implement and understand Algorithms for Graph Traversal
17:06
LO4: Apply Graph Theory to Solve Problems in Network Flow
15:22
LO5: Knowledge Check
15:00
Case Study: Graphs
15:00
Topic 11: Trees
02:39
LO1: Understand the Properties of Trees
19:56
LO2: Explore and implement Algorithms Related to Trees
10:29
LO3: Analyze the Structure of Trees and their Applications
08:24
LO4: Knowledge Check
15:00
Case Study: Trees
15:00
Topic 12: Boolean Algebra
03:06
LO1: Understand the Fundamentals of Boolean Algebra
14:40
LO2: Simplify Boolean Expressions using Identities and Algebraic Manipulation
13:26
LO3: Explore the Applications of Boolean Algebra in Digital Logic Design
19:11
LO4: Understand and Design Basic Combinational Circuits using Boolean Expressions
07:21
LO5: Knowledge Check
15:00
Case Study: Boolean Algebra
15:00
Topic 13: Modeling Computation
02:40
LO1: Understand the Basic models of Computation
15:51
LO2: Analyze the Complexity of Algorithms using Models of Computation
08:03
LO3: Apply Concepts of Formal Languages and Automata Theory in problem-solving
07:34
LO4: Knowledge Check
15:00
Case Study: Modeling Computation
15:00
Module Based Quiz
01:00:00
Exam
0/1
Final Exam
01:15:00
Analyst Programmer_AP107: Mathematical Foundations for AI
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