Applied Mathematical Methods for Computing

Applied Mathematical Methods for Computing

This course is part of Essential Mathematics for Computer Science Specialization

Instructor: Omar Karakchi

Access provided by Toshiba Software India

4 modules

Gain insight into a topic and learn the fundamentals.

Beginner level

Recommended experience

2 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

4 modules

Gain insight into a topic and learn the fundamentals.

Beginner level

Recommended experience

2 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

Apply algebra, vectors, and matrices to represent data, model transformations, and solve computational problems.
Work with sequences and series, understanding convergence and applying summation techniques in computing contexts.
Use combinatorial methods, including permutations and combinations, to analyse arrangements, counts, and algorithm behaviour.
Apply probability and statistical reasoning to interpret data, model uncertainty, and support computational decision-making.

Skills you'll gain

Details to know

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Assessments

24 assignments

Taught in English

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This course is part of the Essential Mathematics for Computer Science Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 4 modules in this course

Mathematics underpins every aspect of computing, from algorithms and artificial intelligence to data analysis and cryptography. Applied Mathematical Methods for Computing equips you with essential tools in algebra, vectors, matrices, sequences, series, combinatorics, probability, and statistics. These methods provide the structure and reasoning needed to solve complex computational problems. Across four modules, you’ll explore advanced techniques, practise solving real-world examples, and build the confidence to apply mathematics in programming, algorithms, and data science. By the end, you’ll have a comprehensive toolkit for modelling systems, analysing uncertainty, and reasoning rigorously about computational tasks. Whether you’re preparing for advanced studies in computer science or strengthening your foundations for professional roles, this course offers the mathematical depth you need to succeed.

In this module, we will introduce algebra, vectors and matrices. This week, we will introduce vectors and vector spaces and look at how to perform basic operations with vectors. We will then introduce linear transformations and their representation via matrices. We will use matrices to describe and capture geometrical transformations (rotations, contractions, shear and projections). We will use a trick (using an extra dimension) to deal with translations.

What's included

13 videos3 readings5 assignments

13 videos Total 89 minutes

Introduction to the course 1 minute
Introduction to vectors 7 minutes
Scalar product (dot product) 13 minutes
Cross product 6 minutes
Introduction to matrices 5 minutes
Operations with matrices 6 minutes
The determinant and inverse of 2 by 2 matrices 7 minutes
Transformations with 2 by 2 matrices – enlargement 4 minutes
Transformations with 2 by 2 matrices –reflection 4 minutes
Transformations with 2 by 2 matrices – rotation 6 minutes
Transformations with 2 by 2 matrices – shearing 4 minutes
Homogenous coordinates 15 minutes
Gaussian elimination 10 minutes

3 readings Total 40 minutes

Course structure and navigation 15 minutes
How to learn effectively on this course 15 minutes
Course Syllabus 10 minutes

5 assignments Total 140 minutes

Check your understanding: End of module 1 20 minutes
Vectors and vector spaces 30 minutes
Matrices 30 minutes
2 by 2 matrices 30 minutes
Homogeneous coordinates 30 minutes

In this module, we will cover the key concepts of sequences, series and the principle of mathematical induction. We will understand what a sequence is and look at its convergence and divergence. We will also introduce the concept of series.

What's included

11 videos9 assignments

11 videos Total 84 minutes

Introduction to sequences and series 5 minutes
Geometric and arithmetic series 8 minutes
Convergent and divergent sequences 6 minutes
Series 7 minutes
Formula for summing geometric and arithmetic sequences 15 minutes
Introduction to proofs 8 minutes
The principle of mathematical induction 4 minutes
Proof by induction 8 minutes
Recursive definitions 6 minutes
Recurrence relations 9 minutes
Solving recurrence relations 8 minutes

9 assignments Total 260 minutes

Check your understanding: End of module 2 20 minutes
Introduction to sequences 30 minutes
Sequences and series 30 minutes
Introduction to proofs 30 minutes
The principle of mathematical induction 30 minutes
Proof by induction 30 minutes
Recursive definitions 30 minutes
Recurrence relations 30 minutes
Solving recurrence relations 30 minutes

In this module, we will cover the following key concepts: counting, permutations, combinations, inclusions, exclusions and the Pigeonhole Principle.

What's included

9 videos2 readings7 assignments1 discussion prompt

9 videos Total 43 minutes

Introduction 1 minute
Counting 5 minutes
Complex counting 5 minutes
The Pigeonhole Principle 3 minutes
The Pigeonhole Principle – examples part 1 5 minutes
The Pigeonhole Principle – examples part 2 4 minutes
Permutations 7 minutes
Combinations 10 minutes
Conclusion 4 minutes

2 readings Total 70 minutes

Exercises with hints and tips 60 minutes
Exercises with hints and tips 10 minutes

7 assignments Total 195 minutes

Check your understanding: End of module 3 20 minutes
Counting 35 minutes
Use the Pigeonhole Principle 25 minutes
Permutations - solving a case study of your choice 30 minutes
Permutations 20 minutes
No order/combinations 25 minutes
Combinatorics 40 minutes

1 discussion prompt Total 20 minutes

Think of an example 20 minutes

This week, we will introduce basic concepts of statistics. We will look at how to estimate probabilities from data and how to define and extract important measures from data, like mean, median and variance.