Ce cours fait partie de la Spécialisation Introduction to Computer Science and Programming

Mathematics for Computer Science

proposé par

Université de Londres

Goldsmiths, Université de Londres

Dans le cadre du diplôme Bachelor of Science in Computer Science

Spécialisation Introduction to Computer Science and Programming

Université de Londres

À propos de ce cours

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“Welcome to Introduction to Numerical Mathematics. This is designed to give you part of the mathematical foundations needed to work in computer science in any of its strands, from business to visual digital arts, music, games. At any stage of the problem solving and modelling stage you will require numerical and computational tools. We get you started in binary and other number bases, some tools to make sense of sequences of numbers, how to represent space numerical using coordinates, how to study variations of quantities via functions and their graphs. For this we prepared computing and everyday life problems for you to solve using these tools, from sending secret messages to designing computer graphics. 
If you wish to take it further you can join the BSc Computer Science degree and complete the full module ‘Numerical Mathematics’. 
Enjoy!”

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Spécialisation Introduction to Computer Science and Programming

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Niveau débutant

Approx. 35 heures pour terminer

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Anglais

Sous-titres : Anglais

Ce que vous allez apprendre

1. Transform numbers between number bases and perform arithmetic in number bases

2. Identify, describe and compute sequences of numbers and their sums.

3. Represent and describe space numerically using coordinates and graphs.

4. Study, represent and describe variations of quantities via functions and their graphs.

Cours 3 sur 3 dans le

Spécialisation Introduction to Computer Science and Programming

100 % en ligne

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.

Niveau débutant

Approx. 35 heures pour terminer

Recommandé : 14 hours/week...

Anglais

Sous-titres : Anglais

Programme du cours : ce que vous apprendrez dans ce cours

Semaine

9 heures pour terminer

Number Bases - Binary

In this week, we will cover the key concepts: Place value and Number systems. You will learn about the notion of number bases, how to do operate in binary.

13 vidéos (Total 137 min), 6 lectures, 9 quiz

13 vidéos

0.001 Overview of using Numerical Mathematics in Computing6 min

1.001 Introduction to number bases and modular arithmetic17 min

1.101 Introduction to number bases17 min

1.103 Place value for integers: binary to decimal7 min

1.105 Place value for integers: decimal to binary4 min

1.107 Place value for fractional numbers: binary9 min

1.109 Rational and irrational numbers: decimal and binary20 min

1.114 Summary of binary system and getting ready for operations in binary53s

1.201 Addition in binary4 min

1.203 Subtraction in binary5 min

1.205 Multiplication in binary6 min

1.208 Review of Tasks 1 and 235 min

1.210 Summary and context of binary in computing48s

6 lectures

Acknowledgements1 min

0.003 Technical requirements10 min

0.004 Optional reading1 min

1.003 Number Bases Summative Quiz1 h

1.112 Task 1: Algorithm for translation between decimal and binary10 min

1.300 Number Bases Summative Quiz30 min

8 exercices pour s'entraîner

1.102 Identifying number bases10 min

1.104 Integer binary to decimal20 min

1.106 Translating from decimal to binary (integers)20 min

1.108 Translating between decimal and binary fractional numbers15 min

1.110 Rational and irrational numbers: decimal and binary15 min

1.202 Addition in binary15 min

1.204 Subtraction in binary15 min

1.206 Multiplication in binary15 min

Semaine

8 heures pour terminer

NUMBER BASES - other bases

In this week, we will extend the place value and number systems to Octal, Hexadecimal and any other bases. You will also be introduced to the usefulness of hexadecimal in computer science.

7 vidéos (Total 78 min), 1 lecture, 7 quiz

7 vidéos

2.101 Octal and hexadecimal (integer)13 min

2.103 Octal and hexadecimal (fractional)11 min

2.105 Special relationship between binary and hexadecimal, and binary and octal12 min

2.201 Hidden messages inside an image21 min

2.301 Arithmetic in hexadecimal/octal8 min

2.303 Other bases9 min

2.401 Summary1 min

1 lectures

2.203 Task 3: Steganography – instructions15 min

6 exercices pour s'entraîner

2.102 Translate between decimal and octal or hexadecimal (integer)40 min

2.104 Translate between decimal and hexadecimal or octal (fractional)20 min

2.106 Translate between binary and hexadecimal/octal40 min

2.302 Arithmetic in hexadecimal/octal1 h

2.304 Other bases5 min

2.401 Number Bases Summative Quiz1 h

Semaine

8 heures pour terminer

Modular arithmetic

In this week, we will cover the key concept of congruence modulo an integer. You will also be introduced to the usefulness of congruence and modular arithmetic operations in computer science.

9 vidéos (Total 111 min), 3 lectures, 10 quiz

9 vidéos

3.001 Introduction to modular arithmetic10 min

3.102 Computing n mod k13 min

3.104 Addition mod k7 min

3.106 Additive identity and inverse mod k8 min

3.201 Multiplication mod k9 min

3.204 Multiplicative identity, inverse mod k, exponentiation mod k31 min

3.206 Mod, rem and division5 min

3.301 Encryption using modular arithmetic20 min

3.401 Summary4 min

3 lectures

3.002 Instruction on the summative quiz

3.003 Modular Arithmetic Summative Quiz30 min

3.302 Task 5: Encryption using modular arithmetic – instructions20 min

9 exercices pour s'entraîner

3.101 Clock arithmetic5 min

3.103 Computing n mod k15 min

3.105 Addition mod k12 min

3.108 Computing additive inverses mod k25 min

3.203 Multiplication mod k15 min

3.205 Computing multiplicative inverses mod k; exponentiation mod k30 min

3.207 Use the operator ‘rem’10 min

3.402 Modular Arithmetic Summative Quiz40 min

Josephus problem30 min

Semaine

5 heures pour terminer

Sequences

In this week, we will cover the key concept of number sequences. You will look into more detail at a special family of sequences, called progressions, and study arithmetic and geometric progressions.

8 vidéos (Total 72 min), 6 lectures, 5 quiz

8 vidéos

4.001 Introduction to Sequences and Series11 min

4.101 Introduction to sequences of numbers6 min

4.103 Defining sequences17 min

4.201 Arithmetic progressions8 min

4.203 Geometric progressions12 min

4.301 ISO Paper format7 min

4.305 Task 7: Investigating random numbers8 min

4.401 Summary of Sequences and preparation for next week.1 min

6 lectures

4.002 Instruction to the summative quiz

4.003 Sequences and Series Summative Quiz30 min

4.004 Optional reading2 min

4.302 Task 6: Investigating ISO paper format – instructions5 min

4.307 Task 7: Generating random numbers – instructions10 min

4.402 Sequences and Series Summative Quiz30 min

4 exercices pour s'entraîner

4.102 Patterns in sequences10 min

4.104 Defining sequences and terms5 min

4.202 Working with arithmetic progressions20 min

4.204 Geometric progressions; sequences15 min

Semaine

5 heures pour terminer

Series

In this week, we will cover the key concept of number series, building on number sequences. You will look into more detail at a special family of series arising from arithmetic and geometric progressions. You will look at expression summations of sequences using a compact form with a summation symbol.

10 vidéos (Total 121 min), 8 quiz

10 vidéos

5.101 Series: sums of terms of sequences; summation symbol: sigma notation25 min

5.104 Finite sum of arithmetic sequences7 min

5.106 Finite sum of geometric sequences12 min

5.108 Finite sums10 min

5.111 Summary of series; infinite sequences and sums1 min

5.201 Patterns in infinite sequences; limit; convergence and divergence22 min

5.204 Patterns in series; limit; convergent and divergent series21 min

5.206 Criteria for identifying convergent/ divergent sequence and series14 min

5.209 Summary of Convergence1 min

5.301 Summary of Sequences and Series3 min

8 exercices pour s'entraîner

5.103 Series: sums of terms of sequences; summation symbol: sigma notation20 min

5.105 Finite sum of arithmetic sequences5 min

5.107 Finite sum of geometric sequences10 min

5.110 Finite sums10 min

5.202 Limits of sequences10 min

5.205 Limits of series15 min

5.208 Criteria for identifying convergent/divergent sequences and series10 min

5.302 Sequences and Series Summative Quiz1 h

Semaine

10 heures pour terminer

Introduction to Graph Sketching and Kinematics

In this week, we will cover the key concept of coordinate system, functions and graphical representation of functions, and kinematics. You will look at the example of modelling motion.

18 vidéos (Total 149 min), 6 lectures, 7 quiz

18 vidéos

6.001 Introduction to graph sketching and kinematics2 min

6.101 Cartesian coordinates16 min

6.105 Spiral15 min

6.201 Introduction to functions and graphs4 min

6.204 Functions and tables of values16 min

6.206 Plotting graphs by hand - aspects to consider2 min

6.207 Plotting graphs by hand – straight lines5 min

6.208 Plotting graphs by hand - quadratics10 min

6.209 Plotting graphs by hand - cubics8 min

6.210 Plotting graphs by hand – higher order polynomials4 min

6.211 Plotting graphs by hand – reciprocal8 min

6.212 Plotting graphs by hand – rational functions4 min

6.213 Plotting graphs by hand - piecewise3 min

6.301 Transformations of graphs26 min

6.307 Summary of graphs1 min

6.401 Kinematic equations13 min

6.403 Summary of kinematics1 min

6.501 Summary2 min

6 lectures

6.002 Instruction on the summative quiz

6.003 Graph Sketching and Kinematics Summative Quiz30 min

6.004 Optional reading

6.106 Task 8: Spiral: Instructions10 min

6.214 Instructions for Task 10: graph plotting and sketching by hand10 min

6.305 Instruction for Task 11: grouping functions using transformations of graphs10 min

5 exercices pour s'entraîner

6.104 Cartesian coordinates and conditions15 min

6.205 Graphs and tables of values15 min

6.302 Transformations of graphs15 min

6.402 Kinematic equations15 min

6.502 Graphs of Functions and Kinematics Summative Quiz1 h

Enseignants

Dr Matthew Yee-King

Lecturer

Computing Department, Goldsmiths, University of London

Dr Sara Santos

Lecturer of Mathematics

Computing Department, Goldsmiths, University of London

Commencez à travailler pour obtenir votre master

Ce cours fait partie du diplôme intégralement en ligne Bachelor of Science in Computer Science de Université de Londres. Si vous êtes admis au programme complet, vos cours sont pris en compte dans votre apprentissage diplômant.

À propos de Université de Londres

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À propos de Goldsmiths, Université de Londres

Championing research-rich degrees that provoke thought, stretch the imagination and tap into tomorrow’s world, at Goldsmiths we’re asking the questions that matter now in subjects as diverse as the arts and humanities, social sciences, cultural studies, computing, and entrepreneurial business and management. We are a community defined by its people: innovative in spirit, analytical in approach and open to all....

À propos de la Spécialisation Introduction to Computer Science and Programming

This specialisation covers topics ranging from basic computing principles to the mathematical foundations required for computer science. You will learn fundamental concepts of how computers work, which can be applied to any software or computer system. You will also gain the practical skillset needed to write interactive, graphical programs at an introductory level. The numerical mathematics component will provide you with numerical and computational tools that are essential for the problem solving and modelling stages of computer science....

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