Essential Mathematics for Computer Science

University of London via Coursera Specialization

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Overview

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The Essential Mathematics for Computer Science specialisation provides the fundamental toolkit needed to excel in computing, data science, and software engineering. Across five courses, you will progress from core mathematical foundations to advanced topics that underpin modern computer science. You’ll begin with sets, number systems, functions, and relations, move into advanced mathematical methods such as algebra, vectors, combinatorics, and probability, then explore geometry, trigonometry, and calculus for modelling motion and change. The pathway continues with logic and reasoning, where you’ll master propositional and predicate logic, Boolean algebra, and proof strategies, before concluding with algorithms and complexity, analysing efficiency, recursion, and computational limits. By completing this specialisation, you will gain industry-relevant skills in discrete mathematics, logic, algebra, calculus, probability, and algorithmic reasoning. These competencies prepare you to design efficient algorithms, analyse complexity, reason formally, and apply mathematical methods to real computing challenges. Whether your goal is to pursue further study in computer science, strengthen your programming and problem-solving skills, or advance in fields such as data science, artificial intelligence, or systems design, this specialisation ensures you have the rigorous mathematical foundation that employers and universities expect.

Syllabus

Course 1: Mathematical Foundations for Computing
Course 2: Applied Mathematical Methods for Computing
Course 3: Geometry and Calculus for Computing
Course 4: Logic and Reasoning for Computing
Course 5: Algorithms and Complexity

Courses

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19 hours 14 minutes
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Algorithms and complexity are at the heart of computer science, shaping how we design solutions and measure efficiency. This course provides a rigorous introduction to both the theory and practice of algorithms. You’ll begin with automata theory, exploring how machines recognise and process languages. You’ll then move into practical algorithmic techniques, including searching and sorting, before learning to design and evaluate recursive and iterative algorithms. Finally, you’ll study complexity theory, developing the ability to classify problems and understand computational limits. By combining abstract models with real-world techniques, this course equips you to design algorithms, assess performance, and reason about scalability. Whether you’re pursuing studies in computer science, preparing for a programming role, or aiming to strengthen your technical foundations, you’ll gain both theoretical insight and practical skills for tackling computing challenges.
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19 hours 20 minutes
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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.
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15 hours 14 minutes
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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.
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18 hours 6 minutes
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Logic forms the backbone of computer science, providing the language and methods for precise reasoning, rigorous analysis, and formal proof. Logic and Reasoning for Computing equips learners with essential tools to represent statements, analyse arguments, and verify correctness. Across four modules—Propositional Logic, Predicate Logic, Boolean Algebra, and Proof Techniques—you will build a solid foundation in formal reasoning and connect abstract concepts directly to computing practice. You’ll explore truth tables, quantifiers, Boolean operations, and methods of proof, applying them to areas such as programming, digital circuits, and algorithm verification. By the end of this course, you’ll not only be able to reason critically and communicate arguments clearly, but also have the confidence to apply logical structures to both theoretical and practical problems in computer science.
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19 hours 53 minutes
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Mathematics provides the formal structures and reasoning tools that underpin computer science. Mathematical Foundations for Computing introduces core topics essential for problem-solving, algorithm design, and theoretical computing. You will explore sets and set theory, number systems and bases, functions, and relations—building a toolkit to model data, describe systems, and reason about computational processes. Each module connects abstract mathematics to practical computing contexts, from binary representation and function mapping to relational models. By the end of the course, you will not only understand these concepts theoretically but also know how to apply them to programming, algorithms, and data structures. This course is part of the Essential Mathematics for Computer Science specialisation, preparing you for advanced topics in logic, algorithms, and computational complexity.