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

Included with

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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

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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 videosTotal 89 minutes

Introduction to the course1 minute
Introduction to vectors7 minutes
Scalar product (dot product)13 minutes
Cross product6 minutes
Introduction to matrices5 minutes
Operations with matrices6 minutes
The determinant and inverse of 2 by 2 matrices7 minutes
Transformations with 2 by 2 matrices – enlargement4 minutes
Transformations with 2 by 2 matrices –reflection4 minutes
Transformations with 2 by 2 matrices – rotation6 minutes
Transformations with 2 by 2 matrices – shearing4 minutes
Homogenous coordinates15 minutes
Gaussian elimination10 minutes

3 readingsTotal 40 minutes

Course structure and navigation15 minutes
How to learn effectively on this course15 minutes
Course Syllabus10 minutes

5 assignmentsTotal 140 minutes

Vectors and vector spaces30 minutes
Matrices 30 minutes
2 by 2 matrices30 minutes
Homogeneous coordinates30 minutes
Check your understanding: End of module 120 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 videosTotal 84 minutes

Introduction to sequences and series 5 minutes
Geometric and arithmetic series8 minutes
Convergent and divergent sequences6 minutes
Series7 minutes
Formula for summing geometric and arithmetic sequences15 minutes
Introduction to proofs8 minutes
The principle of mathematical induction4 minutes
Proof by induction8 minutes
Recursive definitions6 minutes
Recurrence relations9 minutes
Solving recurrence relations8 minutes

9 assignmentsTotal 260 minutes

Introduction to sequences 30 minutes
Sequences and series30 minutes
Introduction to proofs30 minutes
The principle of mathematical induction30 minutes
Proof by induction30 minutes
Recursive definitions30 minutes
Recurrence relations30 minutes
Solving recurrence relations30 minutes
Check your understanding: End of module 220 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 videosTotal 43 minutes

Introduction1 minute
Counting5 minutes
Complex counting5 minutes
The Pigeonhole Principle3 minutes
The Pigeonhole Principle – examples part 15 minutes
The Pigeonhole Principle – examples part 24 minutes
Permutations7 minutes
Combinations10 minutes
Conclusion4 minutes

2 readingsTotal 70 minutes

Exercises with hints and tips60 minutes
Exercises with hints and tips10 minutes

7 assignmentsTotal 195 minutes

Counting35 minutes
Use the Pigeonhole Principle25 minutes
Permutations - solving a case study of your choice30 minutes
Permutations20 minutes
No order/combinations25 minutes
Combinatorics40 minutes
Check your understanding: End of module 320 minutes

1 discussion promptTotal 20 minutes

Think of an example20 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 videosTotal 40 minutes

Introduction to probability12 minutes
Introducing statistics10 minutes
Worked examples (socks from a drawer)8 minutes
Sharing birthdays6 minutes
Looking back3 minutes
Course summary1 minute

1 readingTotal 10 minutes

Advanced Mathematical Methods for Computing: Course Summary10 minutes

3 assignmentsTotal 80 minutes

Probability 30 minutes
Statistics30 minutes
Check your understanding: End of module 420 minutes

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Instructor

Omar Karakchi

University of London

7 Courses48,453 learners

Offered by

University of London

Goldsmiths, University of London

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