Geometry and Calculus for Computing
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Geometry and Calculus for Computing
This course is part of Essential Mathematics for Computer Science Specialization
Instructor: Omar Karakchi
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What you'll learn
Solve geometric and trigonometric problems involving angles, lines, and triangles, applying them to computing contexts.
Sketch and interpret graphs of functions and apply kinematics to describe displacement, velocity, and acceleration.
Work with exponential and logarithmic functions, exploring their rules, graphs, and applications in computational systems.
Understand limits and apply differentiation to calculate gradients, sketch curves, and solve optimisation problems.
Details to know
February 2026
17 assignments
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There are 4 modules in this course
Mathematics provides the foundation for reasoning, problem-solving, and analysis in computer science. Geometry and Calculus for Computing equips you with essential tools to model shapes, describe motion, and analyse change. Across four modules, you’ll build a solid grounding in trigonometry, graph sketching, kinematics, exponential and logarithmic functions, and introductory calculus. You’ll learn to connect abstract mathematical concepts to practical computing applications, from computer graphics and simulations to optimisation and algorithm analysis. By the end of the course, you’ll have the skills to interpret functions, calculate gradients, and apply mathematical reasoning to a wide range of computational problems. This course prepares you for advanced study in computer science and data science by strengthening the mathematical toolkit you need to succeed in both academic and professional contexts.
In this module, we will look at angles, triangles and trigonometry. We will study trigonometric ratios on different triangles, we will work with triangles that are not necessarily right-angled and we will use the sine, cosine and tangent rules relating to the lengths and angles of a triangle. We will also look at Pythagoras' theorem and use it in conjunction with trigonometric ratios.
What's included
9 videos4 readings5 assignments
9 videos•Total 83 minutes
- Introduction to the course•1 minute
- Introduction to triangles and trigonometry•16 minutes
- The circle•8 minutes
- From the circle to the sine and cosine graphs•10 minutes
- Introducing the tangent•6 minutes
- Applications of sine and cosine rules – examples•10 minutes
- Unit circumference and definition of trigonometric functions for every angle•10 minutes
- Plotting tan•2 minutes
- Trigonometric functions, plots and properties•20 minutes
4 readings•Total 50 minutes
- Course structure and navigation•15 minutes
- How to learn effectively on this course•15 minutes
- Course Syllabus•10 minutes
- Summary•10 minutes
5 assignments•Total 140 minutes
- Check your understanding: End of module 1•20 minutes
- Introduction to triangles and trigonometry•30 minutes
- Sine and cosine rules•30 minutes
- Unit circumference and definition of trigonometric functions for every angle•30 minutes
- Trigonometric functions, plots and properties•30 minutes
In this module, we will learn about three concepts: the definition of a function, Cartesian coordinates and the graph of a function. We will use these concepts to describe simple motion (kinematics).
What's included
9 videos2 readings4 assignments
9 videos•Total 70 minutes
- Definition of a function and Cartesian coordinates•14 minutes
- The inverse of a function•4 minutes
- Plotting linear functions on a Cartesian plane•7 minutes
- Plotting quadratic functions on the Cartesian plane•9 minutes
- Higher-order functions and limits•17 minutes
- Transformations of functions•3 minutes
- Using Desmos•3 minutes
- Introduction to kinematics and the laws of motion•11 minutes
- Kinematics – worked examples •3 minutes
2 readings•Total 40 minutes
- Testing Desmos•30 minutes
- Summary•10 minutes
4 assignments•Total 125 minutes
- Check your understanding: End of module 2•20 minutes
- Definition of a function and Cartesian coordinates•45 minutes
- Higher-order polynomials•30 minutes
- Kinematics•30 minutes
In this topic (weeks 13 and 14), we will look at exponential and logarithmic functions. This week, we will introduce the exponential functional as extension of elevation to a non-integer power, we derive its properties and plot.
What's included
8 videos3 assignments
8 videos•Total 42 minutes
- Exponential function, definition, plot and properties – properties•9 minutes
- Exponential function, definition, plot and properties – graphs•7 minutes
- Exponential function, definition, plot and properties – identity•3 minutes
- Logarithmic function, definition, plot and properties – algebra•11 minutes
- Logarithmic function, definition, plot and properties – graphs•5 minutes
- Logarithmic function, definition, plot and properties – equations•3 minutes
- Solving equations involving exp and log•2 minutes
- Topic 7 – looking back•2 minutes
3 assignments•Total 80 minutes
- Check your understanding: End of module 3•20 minutes
- Exponential functions•30 minutes
- Logarithmic functions•30 minutes
In this topic (weeks 15 and 16), we will focus on limits and differentiation. This week, we will look at limits of a function and discuss the concept of continuity of a function. We will then introduce a new tool, differentiation and derive the derivative of common functions from first principles.
What's included
12 videos1 reading5 assignments
12 videos•Total 74 minutes
- Continuous and discontinuous functions•10 minutes
- Binomial expansion•7 minutes
- Introducing differentiation•10 minutes
- Worked examples•3 minutes
- Examples of differentiating polynomials•6 minutes
- Worked examples of differentiation•13 minutes
- Differentials of key functions•3 minutes
- The product rule•7 minutes
- The quotient rule•4 minutes
- The chain rule•7 minutes
- Topic 8 – looking back•2 minutes
- Course summary•1 minute
1 reading•Total 10 minutes
- Geometry and Calculus for Computing: Course Summary•10 minutes
5 assignments•Total 140 minutes
- Check your understanding: End of module 4•20 minutes
- Continual expansion and binomial differentiation•30 minutes
- Further differentiation I•30 minutes
- Differentiating polynomials•30 minutes
- Further differentiation II – product, quotient and chain rule•30 minutes
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