Applied Mathematical Methods for Computing
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Applied Mathematical Methods for Computing
This course is part of Essential Mathematics for Computer Science Specialization
Instructor: Omar Karakchi
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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.
Details to know
February 2026
24 assignments
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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.
What's included
6 videos1 reading3 assignments
6 videos•Total 40 minutes
- Introduction to probability•12 minutes
- Introducing statistics•10 minutes
- Worked examples (socks from a drawer)•8 minutes
- Sharing birthdays•6 minutes
- Looking back•3 minutes
- Course summary•1 minute
1 reading•Total 10 minutes
- Advanced Mathematical Methods for Computing: Course Summary•10 minutes
3 assignments•Total 80 minutes
- Check your understanding: End of module 4•20 minutes
- Probability •30 minutes
- Statistics•30 minutes
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