S1 2026 MAT 101 - Intermediate Algebra

MAT101 – Intermediate Algebra Study Notes

Acknowledgements

  • Contribution from:

    • Malata, H – MSc. Mathematical Sciences

Course Information

Course Title

  • MAT101 – Intermediate Algebra

Required Texts

  • NU MAT 101 Course Material Standards

  • Michael, S. Michael, S III. (2023). College Algebra: Concepts Through Functions, Pearson Prentice Hall, USA

  • Jerome E. Kaufmann, K. L. (n.d.). Algebra for College Students. Thomson Brooks/Cole.

  • John Bird (2006). Higher Engineering Mathematics 5th Edition. Elsevier Ltd.

Recommended Texts

  • Michael, S. (2023). College Algebra: Concepts Through Functions, Pearson Prentice Hall, USA

  • Kaufmann, J. E. (n.d.). Algebra for College Students. Thomson Brooks/Cole.

Instructor Details

  • Name: Hedson Malata

  • Email: hedson.malata@northrise.net

  • Biography:

    • Hedson Malata holds a Bachelor of Science in Mathematics Education from Copperbelt University (CBU) and a Master of Science in Mathematical Sciences from the African Institute for Mathematical Sciences (AIMS) in Rwanda. His interests lie in applications of scientific computing, mathematical and statistical modelling, and machine learning in climate and finance.

Course Overview

  • Introduces students to fundamental and advanced concepts in introductory mathematics, emphasizing algebra, geometry, and trigonometry.

  • Develops mathematical foundation, analytical reasoning, logical thinking, and structured problem-solving skills.

  • Explores mathematical principles used to describe patterns, relationships, and quantitative processes in real-world contexts.

  • Encourages confidence in working with symbolic expressions, equations, graphical representations, and numerical relationships.

  • Develops skills in translating real-world situations into mathematical forms, selecting appropriate solution methods, and interpreting results.

  • Promotes independent learning and intellectual curiosity by encouraging exploration of multiple solution methods and reflection on efficiency.

  • Introduces basic technological tools supporting mathematical calculations, visualization, and data interpretation.

  • Aims to equip students with transferable quantitative and analytical skills for higher-level study and practical applications across various academic disciplines and professional fields.

Prerequisites

  • None

Credits

  • 3

Course Objectives

  1. Strengthen foundational understanding of algebraic concepts.

  2. Develop ability to apply fundamental principles of algebra in problem-solving.

  3. Understand the concept of functions, including properties and applications.

  4. Analyze and interpret graphs of algebraic and transcendental functions.

  5. Promote application of algebraic and functional concepts in computational and analytical problem-solving.

Course Policies

Attendance and Participation

  • Students are expected to attend at least 70% of all lectures and be punctual.

  • Importance placed on reading and understanding modules and assignments.

  • Responsibility to ask questions when needed, in class or via email/phone.

Instructional Approach

  • Lectures will be conducted in “dialogue” form focused on collaboration and discussion.

Assignments

  • Must be written in APA format. Submission deadlines are strict, with penalties for late submissions.

Grading Policy

  • Total possible points calculated throughout the course with awarded letter grades based on points.

Course Schedule Overview

Week 1

  • Session 1: Set Theory

  • Session 2: Sets of Numbers

Week 2

  • Session 3: Sets of Numbers II

  • Session 4: Functions I

Week 3

  • Session 5: Functions II

  • Session 6: Quadratic Functions

Week 4

  • Session 7: Quadratic Functions II

  • Session 8: Polynomial Functions I

Week 5

  • Session 9: Polynomial Functions II

  • Session 10: Rational Functions and Absolute Value Functions

Week 6

  • Session 11: Sequences and Series

  • Session 12: Mathematical Induction and Partial Fraction Decomposition

Week 7

  • Session 13: Binomial Theorem

  • Session 14: Matrices I

Weeks 8-12: Exams and Review
Week 13: Course Review
Week 14: Study Week
Week 15 & 16: Exam Weeks

Course Modules

Week 1: Set Theory
Required Reading

  • Boules, A. N. (2021). Fundamentals of Mathematical Analysis.

  • Haggarty, R. (1993). Fundamentals of Mathematical Analysis.

Learning Objectives

  • Define sets and types: Basic set notation, including union, intersection, etc.

  • Perform basic operations: Such as union, intersection, and subsets with examples drawn from real-life.

  • State and prove De Morgan’s Laws: Representing logically through symbolic reasoning and Venn diagrams.

  • Define Cartesian products: Apply to set representation.

Definitions

  • Set: A well-defined collection of distinct objects. Denoted by letters (e.g., A, B).

  • Specifies set using:

    • Listing elements in braces. E.g., {1, 2, 3}.

    • Property notation: {x | property of x}.

  • Subset: A is a subset of B if every member of A is in B, denoted as A ⊆ B.

  • Empty Set: Denoted by Ø or {} and has no elements.

Cardinality and Types of Sets

  • Cardinality: Denoted |A|, refers to the number of elements in a set A. Non-negative integers or infinity.

  • Types of Numbers:

a. Natural Numbers: ℕ = {1, 2, 3…}
- Examples:
- Finite: Ended collections.
- Infinite: Non-ending collections.
- Closed under addition and multiplication.

  • Whole Numbers: ℕ∪{0} = {0, 1, 2…}

  • Integers: ℤ = {…, -3, -2, -1, 0, 1, 2, 3…}

  • Rational Numbers: ℚ = {p/q | p, q ∈ ℤ, q ≠ 0}

  • Irrational Numbers: Cannot be expressed as p/q.

Set Operations

  1. Union: $A igcup B = {x | x ∈ A ext{ or } x ∈ B}$

  2. Intersection: $A igcap B = {x | x ∈ A ext{ and } x ∈ B}$

  3. Difference: $A - B = {x | x ∈ A ext{ and } x ∉ B}$

  4. Disjoint Sets: $A igcap B = Ø$

  5. Power Set: denotes the set of all subsets of A, denoted by 𝒫(A).

Cartesian Products

  • Definition: If A and B are sets, then A × B = {(a, b) | a ∈ A, b ∈ B}. Provides ordered pairs.

Mathematical Statements

  • Statements: A mathematical sentence that is either true or false.

  • Logical Connectives:

    • Negation: ¬P

    • Conjunction: P ∧ Q

    • Disjunction: P ∨ Q

  • Implication: P ⇒ Q
    -

Study Plan for Week 1: Set Theory
Day 1: Introduction to Sets

  • Objective: Define sets and their types

  • Activities:

    • Read Chapter (Session 1)

    • Write down definitions of different types of sets

    • Practice basic set notation and operations

Day 2: Basic Operations with Sets

  • Objective: Understand and perform operations like union and intersection

  • Activities:

    • Read Chapter (Session 2)

    • Solve problems involving union and intersection

    • Create Venn diagrams for visual representation

Day 3: De Morgan’s Laws

  • Objective: Learn to state and prove De Morgan's Laws

  • Activities:

    • Study De Morgan's Laws with examples

    • Write proofs using symbolic reasoning

    • Create Venn diagrams illustrating the laws

Day 4: Cartesian Products

  • Objective: Define and apply Cartesian products

  • Activities:

    • Read relevant section in the textbook

    • Practice problems involving Cartesian products

    • Real-life applications of Cartesian products in ordered pairs

Day 5: Review & Practice Problems

  • Objective: Reinforce concepts learned throughout the week

  • Activities:

    • Go over notes and definitions

    • Solve a variety of practice problems from readings

    • Work with peers to discuss difficult concepts

Day 6: Prepare for Assessment

  • Objective: Review all materials in preparation for the test

  • Activities:

    • Review flashcards

    • Practice explaining concepts to someone else

    • Take a self-assessment quiz

Day 7: Rest Day/Last Minute Review

  • Objective: Relax and do light review if necessary

  • Activities:

    • Briefly go over key concepts and definitions

    • Avoid heavy studying to prevent burnout.