Analyst Programmer_AP107: Mathematical Foundations for AI (Professional)

About Course

The main purpose of this course is to lay:

The mathematical foundations required for success in other program streams such as computer architecture, programming and data base management systems.
Subsequent mathematics courses rely on the discrete mathematics learned in this course.
The students will solve problems using the concepts, structures and methods of discrete mathematics.
The emphasis throughout this course is on acquiring the applied mathematical foundations (e.g. Number systems, matrices, graphs, trees, and combinatorics) upon which computer applications are built.

Upon successful completion of this course, the student will have demonstrated the ability to:

Apply rules and concepts pertaining to different positional number systems (specifically, decimal, binary and hexadecimal).
Covert between decimal, binary and hexadecimal number systems.
Apply notation, vocabulary, operations, and diagramming techniques, pertaining to mathematical sets.
Apply notation, vocabulary, and diagramming techniques, pertaining to graph theory.
Analyze and assess problems pertaining to various types of graphs, directed graphs and trees.
Solve various problems pertaining to graph theory using matrices.
Apply shortest path algorithms to various problems pertaining to graph theory
Apply modulus arithmetic to the solution of practical problems.
Use truth tables to illustrate the logical connectives: AND, OR,XOR, and NOT to evaluate logical expressions.
Use combinatorial circuits to demonstrate the applications of logical expressions in computer science.
Use Karnaugh maps to simplify logical expressions.

Course Content

Module 1

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
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
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
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
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
Topic 6: Counting

03:02
LO1: Understand the Basic Principles of Counting

12:19
LO3: Apply the Binomial Theorem in Solving Counting Problems

06:35
LO4: Understand and Solve problems Using the Pigeonhole Principle

06:22
LO2: Explore Permutations and Combinations and their Applications

11:38
LO5: Knowledge Check
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
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
LO1: Discuss Relations and their Properties

09:05
LO2: Analyze Equivalence Relations and Partitions

10:01
Topic 9: Relations

02:50
LO3: Explore Partial Orderings and their Applications

07:08
LO4: Understand and Construct Hasse Diagrams

11:38
LO5: Knowledge Check
LO1: Understand the fundamental concepts of Graph Theory

10:58
LO2: Analyze Graph Connectivity

08:47
Topic 10: Graphs

02:49
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
LO1: Understand the Properties of Trees

19:56
LO2: Explore and implement Algorithms Related to Trees

10:29
Topic 11: Trees

02:39
LO3: Analyze the Structure of Trees and their Applications

08:24
LO4: Knowledge Check
LO1: Understand the Fundamentals of Boolean Algebra

14:40
LO2: Simplify Boolean Expressions using Identities and Algebraic Manipulation

13:26
Topic 12: Boolean Algebra

03:06
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
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
Module Based Quiz
LO4: Knowledge Check

About Course

Course Content

Module 1

Topic 1: The Foundations: Logic and Proofs

LO1: Understand and Apply Propositional Logic, including Truth Tables

LO2: Discuss Logical Equivalences and Quantifiers

LO3: Analyze and construct Valid Arguments using Rules of Inference

LO4: Differentiate between Direct, Indirect, and Proof by Contradiction Techniques

LO5: Knowledge Check

Topic 2: Basic Structures: Sets, Functions, Sequences, Sums, and Matrices

LO1: Define and perform Operations on Sets

LO2: Understand the concept of Functions

LO3: Analyze Sequences and their properties

LO4: Apply Summation Notation and Compute Sums using Formulas

LO5: Understand the Basics of Matrices, including Matrix Operations and Determinants

LO6: Knowledge Check

Topic 3: Algorithms

LO1: Understand the concept of Algorithms and their Role in Problem-Solving

LO2: Analyze the efficiency of Algorithms using Notations

LO3: Explore various Algorithmic Paradigms

LO4: Elaborate common Algorithms for Sorting, Searching, and Graph Traversal

LO5: Knowledge Check

Topic 4: Number Theory and Cryptography

LO1: Understand the Basic Principles of Number Theory

LO2: Apply the Euclidean Algorithm and Modular Arithmetic in Problem-Solving

LO3: Explore Concepts of Cryptography

LO4: Knowledge Check

Topic 5: Induction and Recursion

LO1: Discuss and apply the Principle of Mathematical Induction

LO2: Understand and apply Strong Induction in more Complex Proofs

LO3: Explore the concept of Recursion and its Relation to Inductive Reasoning

LO4: Knowledge Check

Topic 6: Counting

LO1: Understand the Basic Principles of Counting

LO3: Apply the Binomial Theorem in Solving Counting Problems

LO4: Understand and Solve problems Using the Pigeonhole Principle

LO2: Explore Permutations and Combinations and their Applications

LO5: Knowledge Check

Topic 7: Discrete Probability

LO1: Understand the Basic Principles of Probability

LO2: Calculate Probabilities using Conditional Probability and Independence

LO3: Apply Bayes’ Theorem in Problem-Solving

LO4: Explore Discrete Random Variables and their Expected values

LO5: Knowledge Check

Topic 8: Advanced Counting Techniques

LO1: Discuss Advanced Counting Techniques

LO2: Understand and Apply Recurrence Relations in Solving Counting Problems

LO3: Analyze Problems using the Principle of Inclusion-Exclusion

LO4: Solve Complex Counting Problems using Generating Functions

LO5: Knowledge Check

LO1: Discuss Relations and their Properties

LO2: Analyze Equivalence Relations and Partitions

Topic 9: Relations

LO3: Explore Partial Orderings and their Applications

LO4: Understand and Construct Hasse Diagrams

LO5: Knowledge Check

LO1: Understand the fundamental concepts of Graph Theory

LO2: Analyze Graph Connectivity

Topic 10: Graphs

LO3: Implement and understand Algorithms for Graph Traversal

LO4: Apply Graph Theory to Solve Problems in Network Flow

LO5: Knowledge Check

LO1: Understand the Properties of Trees

LO2: Explore and implement Algorithms Related to Trees

Topic 11: Trees

LO3: Analyze the Structure of Trees and their Applications

LO4: Knowledge Check

LO1: Understand the Fundamentals of Boolean Algebra

LO2: Simplify Boolean Expressions using Identities and Algebraic Manipulation

Topic 12: Boolean Algebra

LO3: Explore the Applications of Boolean Algebra in Digital Logic Design

LO4: Understand and Design Basic Combinational Circuits using Boolean Expressions

LO5: Knowledge Check

Topic 13: Modeling Computation

LO1: Understand the Basic models of Computation

LO2: Analyze the Complexity of Algorithms using Models of Computation

LO3: Apply Concepts of Formal Languages and Automata Theory in problem-solving

Module Based Quiz

LO4: Knowledge Check

Exam