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Applied Mathematical Methods for Computing · LearnSpace
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Applied Mathematical Methods for Computing

Курс от University of London, Goldsmiths, University of London
Начальный≈ 19.6 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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.

Навыки, которые вы освоите

CombinatoricsApplied MathematicsMathematical Theory & AnalysisDescriptive StatisticsProbabilityLinear AlgebraAlgebraStatistical MethodsMathematics and Mathematical ModelingGeometryProbability & StatisticsStatisticsAdvanced MathematicsAlgorithmsStatistical AnalysisData Analysis

Программа курса

4 модулей · 74 учебных материалов

01Algebra, vectors and matrices21 материалов

Lesson 1.0 Introduction

Course structure and navigationЧтениеHow to learn effectively on this courseЧтениеIntroduction to the courseВидеоCourse SyllabusЧтение

Lesson 1.1 Vectors and vector spaces

Учитесь у экспертов

Omar Karakchi

Lecture

Applied Mathematical Methods for Computing
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≈ 19.6 ч

4 модулей

Язык: Английский

Часть программы вашего университета
Introduction to vectorsВидео
Scalar product (dot product)Видео
Cross productВидео
Vectors and vector spacesЗадание

Lesson 1.2 Introducing 2 by 2 matrices

Introduction to matricesВидеоOperations with matricesВидеоMatrices ЗаданиеThe determinant and inverse of 2 by 2 matricesВидеоTransformations with 2 by 2 matrices – enlargementВидеоTransformations with 2 by 2 matrices –reflectionВидеоTransformations with 2 by 2 matrices – rotationВидеоTransformations with 2 by 2 matrices – shearingВидео2 by 2 matricesЗадание

Lesson 1.3: Homogenous coordinates

Homogenous coordinatesВидеоGaussian eliminationВидеоHomogeneous coordinatesЗадание

Lesson 1.4: Summary and Assessments

Check your understanding: End of module 1Задание
02Sequence and Series21 материалов

Lesson 2.1 Introduction to Sequences and Series

Introduction to sequences and series ВидеоGeometric and arithmetic seriesВидеоConvergent and divergent sequencesВидеоIntroduction to sequences ЗаданиеSeriesВидеоFormula for summing geometric and arithmetic sequencesВидеоSequences and seriesЗадание

2.2 Mathematical Induction

Introduction to proofsВидеоIntroduction to proofsЗаданиеThe principle of mathematical inductionВидеоThe principle of mathematical inductionЗаданиеProof by inductionВидеоProof by inductionЗаданиеInvestigate and discuss

Lesson 2.3 Recursion

Recursive definitionsВидеоRecursive definitionsЗаданиеRecurrence relationsВидеоRecurrence relationsЗаданиеSolving recurrence relationsВидеоSolving recurrence relationsЗадание

Lesson 2.4 Summary and Assessments

Check your understanding: End of module 2Задание
03Combinatorics20 материалов

Lesson 3.1 Counting

IntroductionВидеоCountingВидеоComplex countingВидеоCountingЗаданиеInclusion–Exclusion PrincipleDIALOGUE

3.2 The Pigeonhole Principle

The Pigeonhole PrincipleВидеоThe Pigeonhole Principle – examples part 1ВидеоThe Pigeonhole Principle – examples part 2ВидеоUse the Pigeonhole PrincipleЗаданиеThink of an exampleОбсуждениеExercises with hints and tipsЧтение

Lesson 3.3 Order Matters

PermutationsВидеоPermutations - solving a case study of your choiceЗаданиеPermutationsЗаданиеCombinationsВидеоNo order/combinationsЗаданиеCombinatoricsЗадание

3.4 Summary and Assessments

Exercises with hints and tipsЧтениеConclusionВидеоCheck your understanding: End of module 3Задание
04 Probability and Statistics12 материалов

Lesson 4.1 Probability Definition and Properties

Introduction to probabilityВидеоProbability Задание

Lesson 4.2 Statistics

Introducing statisticsВидеоWorked examples (socks from a drawer)ВидеоSharing birthdaysВидеоStatisticsЗадание

Lesson 4.3 Summary and Assessments

Analysing Real-World DataDIALOGUELooking backВидеоCheck your understanding: End of module 4Задание

Course Wrap-up

Advanced Mathematical Methods for Computing: Course SummaryЧтениеThe Ciphered Map: A Cartographic Escape MysteryDIALOGUECourse summaryВидео
DIALOGUE