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

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

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.

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 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 videosTotal 83 minutes

Introduction to the course1 minute
Introduction to triangles and trigonometry16 minutes
The circle8 minutes
From the circle to the sine and cosine graphs10 minutes
Introducing the tangent6 minutes
Applications of sine and cosine rules – examples10 minutes
Unit circumference and definition of trigonometric functions for every angle10 minutes
Plotting tan2 minutes
Trigonometric functions, plots and properties20 minutes

4 readingsTotal 50 minutes

Course structure and navigation15 minutes
How to learn effectively on this course15 minutes
Course Syllabus10 minutes
Summary10 minutes

5 assignmentsTotal 140 minutes

Introduction to triangles and trigonometry30 minutes
Sine and cosine rules30 minutes
Unit circumference and definition of trigonometric functions for every angle30 minutes
Trigonometric functions, plots and properties30 minutes
Check your understanding: End of module 120 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 videosTotal 70 minutes

Definition of a function and Cartesian coordinates14 minutes
The inverse of a function4 minutes
Plotting linear functions on a Cartesian plane7 minutes
Plotting quadratic functions on the Cartesian plane9 minutes
Higher-order functions and limits17 minutes
Transformations of functions3 minutes
Using Desmos3 minutes
Introduction to kinematics and the laws of motion11 minutes
Kinematics – worked examples 3 minutes

2 readingsTotal 40 minutes

Testing Desmos30 minutes
Summary10 minutes

4 assignmentsTotal 125 minutes

Definition of a function and Cartesian coordinates45 minutes
Higher-order polynomials30 minutes
Kinematics30 minutes
Check your understanding: End of module 220 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 videosTotal 42 minutes

Exponential function, definition, plot and properties – properties9 minutes
Exponential function, definition, plot and properties – graphs7 minutes
Exponential function, definition, plot and properties – identity3 minutes
Logarithmic function, definition, plot and properties – algebra11 minutes
Logarithmic function, definition, plot and properties – graphs5 minutes
Logarithmic function, definition, plot and properties – equations3 minutes
Solving equations involving exp and log2 minutes
Topic 7 – looking back2 minutes

3 assignmentsTotal 80 minutes

Exponential functions30 minutes
Logarithmic functions30 minutes
Check your understanding: End of module 320 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 videosTotal 74 minutes

Continuous and discontinuous functions10 minutes
Binomial expansion7 minutes
Introducing differentiation10 minutes
Worked examples3 minutes
Examples of differentiating polynomials6 minutes
Worked examples of differentiation13 minutes
Differentials of key functions3 minutes
The product rule7 minutes
The quotient rule4 minutes
The chain rule7 minutes
Topic 8 – looking back2 minutes
Course summary1 minute

1 readingTotal 10 minutes

Geometry and Calculus for Computing: Course Summary10 minutes

5 assignmentsTotal 140 minutes

Continual expansion and binomial differentiation30 minutes
Further differentiation I30 minutes
Differentiating polynomials30 minutes
Further differentiation II – product, quotient and chain rule30 minutes
Check your understanding: End of module 420 minutes

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Instructor

Omar Karakchi

University of London

7 Courses48,625 learners

Offered by

University of London

Goldsmiths, University of London

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