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Applied Mathematical Methods for Computing

Applied Mathematical Methods for Computing

本课程是 Essential Mathematics for Computer Science 专项课程的一部分

位教师：Omar Karakchi

包含在中

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4个模块

深入了解一个主题并学习基础知识。

初级等级

推荐体验

2 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

4个模块

深入了解一个主题并学习基础知识。

初级等级

推荐体验

2 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

您将学到什么

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.

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要了解的详细信息

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了解顶级公司的员工如何掌握热门技能

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Petrobras, TATA, Danone, Capgemini, P&G 和 L'Oreal 的徽标

积累特定领域的专业知识

本课程是 Essential Mathematics for Computer Science 专项课程专项课程的一部分

在注册此课程时，您还会同时注册此专项课程。

向行业专家学习新概念
获得对主题或工具的基础理解
通过实践项目培养工作相关技能
获得可共享的职业证书

该课程共有4个模块

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.

单元详情

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.

涵盖的内容

13个视频3篇阅读材料5个作业

13个视频总计89分钟

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

3篇阅读材料总计40分钟

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

5个作业总计140分钟

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

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.

涵盖的内容

11个视频9个作业

11个视频总计84分钟

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

9个作业总计260分钟

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

In this module, we will cover the following key concepts: counting, permutations, combinations, inclusions, exclusions and the Pigeonhole Principle.

涵盖的内容

9个视频2篇阅读材料7个作业1个讨论话题

9个视频总计43分钟

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

2篇阅读材料总计70分钟

Exercises with hints and tips60分钟
Exercises with hints and tips10分钟

7个作业总计195分钟

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

1个讨论话题总计20分钟

Think of an example20分钟

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.