Mathematical Induction - Mathematics (Undergraduate Foundation)

Mathematical induction proves a statement is true for every whole number using a starting point and a logical link. It works like a chain reaction where one step confirms the next. This course explains the core principle and applies it to many types of problems. You will study standard series, fractional series, divisibility, and inequalities. The content also covers recursive sequences, matrix powers, and set theory to give you a complete understanding of the method. Programmers use this logic to check that software code works without mistakes. Engineers use it to prove that formulas for structural designs or machines are safe. This skill is vital for anyone in technology, finance, or data science because it makes logical thinking a clear, repeatable process. It removes guesswork and provides the certainty needed for professional work in any technical field. You will learn the three-step induction method to solve different kinds of mathematical proofs. You will prove formulas for series, check if expressions are divisible, and handle difficult inequalities. You will also find general formulas for repeating sequences and solve problems involving matrices and sets. By the end, you will write clear, logical proofs that are required for university mathematics examinations. This course is for university students starting science or engineering degrees and senior secondary school students preparing for higher education. It is also helpful for workers who want to improve their reasoning and problem-solving. Even those not studying mathematics will benefit from the clear way of thinking this course teaches. It provides the basic skills needed for any career that requires logic and proof.

7 hrs

Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
AMS 102: Basic Mathematics
AMS 102: Basic Mathematics
Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings. This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction. You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings. This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction. You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

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DSS 103: Mathematics for Social Scientists I - Algebra and Trigonometry
DSS 103: Mathematics for Social Scientists I - Algebra and Trigonometry
Build the mathematical foundation required to excel in social science degrees and data-driven careers. This track follows the official NUC syllabus for DSS 103 to teach sets, number operations, counting methods, logical proofs, binomial expansions, complex numbers, and trigonometry. Each topic connects directly to the quantitative skills you need for statistics, research methods, and economic analysis. This programme is for first-year university students studying economics, sociology, political science, psychology, geography, or other social science disciplines. It is also for secondary school leavers preparing for university entry and professionals who must strengthen their maths for postgraduate study or analytical roles in government, NGOs, or private sector research. After completing this track, you will solve equations, handle algebraic proofs, manipulate trigonometric formulas, and apply counting principles to real-world data problems. These skills prepare you for advanced coursework in econometrics, statistical analysis, social research, and policy evaluation. You will have the confidence to tackle quantitative modules and compete for roles in banking, public service, consulting, and development work.

Build the mathematical foundation required to excel in social science degrees and data-driven careers. This track follows the official NUC syllabus for DSS 103 to teach sets, number operations, counting methods, logical proofs, binomial expansions, complex numbers, and trigonometry. Each topic connects directly to the quantitative skills you need for statistics, research methods, and economic analysis. This programme is for first-year university students studying economics, sociology, political science, psychology, geography, or other social science disciplines. It is also for secondary school leavers preparing for university entry and professionals who must strengthen their maths for postgraduate study or analytical roles in government, NGOs, or private sector research. After completing this track, you will solve equations, handle algebraic proofs, manipulate trigonometric formulas, and apply counting principles to real-world data problems. These skills prepare you for advanced coursework in econometrics, statistical analysis, social research, and policy evaluation. You will have the confidence to tackle quantitative modules and compete for roles in banking, public service, consulting, and development work.

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MTH 101: Elementary Mathematics I - Algebra and Trigonometry
MTH 101: Elementary Mathematics I - Algebra and Trigonometry
Master the foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science. This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions. Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

Master the foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science. This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions. Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

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Course Chapters

1. Introduction
2
This chapter defines the principle of mathematical induction and its role in formal logic. You will understand the domino effect analogy and why this method is necessary for proving statements across infinite sets of integers. It provides the essential foundation for all subsequent proof techniques in this course. You will master defining the principle of induction, verifying the base case for n equals one, formulating the inductive hypothesis for n equals k, and executing the inductive step to prove the statement for n equals k plus one.
Concept Overviews
2 Lessons
45:31
2. Series
1
3
This chapter focuses on using induction to prove formulas for the sum of arithmetic and geometric sequences. It is the most common application of the method and essential for verifying that a general summation formula holds true for any number of terms. By the end, you will master proving linear and quadratic series identities, applying the inductive hypothesis to algebraic summations, and simplifying complex fractional series expressions to reach the required right-hand side.
Concept Overviews
1 Lesson
17:39
Problem Walkthroughs
3 Lessons
54:49
3. Fractional Series
1
2
This chapter covers proofs for the sums of series with terms written as fractions. It is a vital section because it forces you to use advanced algebraic manipulation and common denominators to link the inductive hypothesis to the final goal. By the end, you will master handling terms with product denominators, using common factors to simplify fractional expressions, and proving telescoping series identities through the inductive step.
Concept Overviews
1 Lesson
6:39
Problem Walkthroughs
2 Lessons
39:22
4. Divisibility
1
3
This chapter teaches how to use induction to prove that algebraic expressions are exactly divisible by specific integers. It is a critical skill for number theory and cryptography, moving beyond simple addition to master the manipulation of factors and remainders in a logical sequence. You will master expressing divisibility as a linear equation, manipulating exponents to isolate common factors, and applying the inductive hypothesis to prove that expressions like n cubed plus 2n are multiples of three.
Concept Overviews
1 Lesson
13:42
Problem Walkthroughs
3 Lessons
39:17
5. Inequalities
1
2
This chapter covers using induction to prove mathematical inequalities where one expression is always greater than another. It is a vital section because it requires logical estimation and transitivity rather than simple equality. This skill is essential for analyzing algorithm efficiency and bounding errors in numerical analysis. You will master handling base cases where n is greater than one, applying the inductive hypothesis to inequalities, and using algebraic estimation to prove that exponential growth eventually exceeds polynomial growth.
Concept Overviews
1 Lesson
9:31
Problem Walkthroughs
2 Lessons
27:18
6. Recursive Sequences
1
3
This chapter applies induction to sequences where each term depends on those before it. It is critical for computer science and engineering because it provides the mathematical proof for how recursive algorithms and loops function. You will learn to verify that a general formula correctly predicts the value of any term in a repeating sequence. You will master defining terms using recurrence relations, proving explicit formulas for recursive sequences, and applying the inductive step to link successive terms.
Concept Overviews
1 Lesson
15:11
Problem Walkthroughs
3 Lessons
44:47
7. Other Problems
2
This chapter covers miscellaneous induction proofs that do not fit into standard categories. It tests your ability to apply logical steps to unfamiliar mathematical structures, ensuring you can use the base case and inductive step on any technical problem. By the end, you will master proving formulas for the nth power of a matrix, calculating total subsets for a set with n elements, and applying inductive logic to non-standard algebraic identities.
Problem Walkthroughs
2 Lessons
31:54