This course is part of the Introduction to Computer Science and Programming Specialization

Offered By

University of London

Goldsmiths, University of London

Introduction to Computer Science and Programming Specialization

University of London

About this Course

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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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Suggested: 13 hours/week...

Subtitles: English

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.

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

Suggested: 13 hours/week...

Subtitles: English

Week

1In 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 videos (Total 137 min), 6 readings, 9 quizzes

1.001 Introduction to number bases and modular arithmetic17m

1.101 Introduction to number bases17m

1.103 Place value for integers: binary to decimal7m

1.105 Place value for integers: decimal to binary4m

1.107 Place value for fractional numbers: binary9m

1.109 Rational and irrational numbers: decimal and binary20m

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

1.201 Addition in binary4m

1.203 Subtraction in binary5m

1.205 Multiplication in binary6m

1.208 Review of Tasks 1 and 235m

1.210 Summary and context of binary in computing48s

0.003 Technical requirements10m

0.004 Optional reading1m

0.005 Acknowledgements1m

1.003 Number Bases Summative Quizs

1.112 Task 1: Algorithm for translation between decimal and binary10m

1.300 Number Bases Summative Quiz30m

1.102 Identifying number bases10m

1.104 Integer binary to decimal20m

1.106 Translating from decimal to binary (integers)20m

1.108 Translating between decimal and binary fractional numbers15m

1.110 Rational and irrational numbers: decimal and binary15m

1.202 Addition in binary15m

1.204 Subtraction in binary15m

1.206 Multiplication in binary15m

Week

2In 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 videos (Total 78 min), 1 reading, 7 quizzes

2.103 Octal and hexadecimal (fractional)11m

2.105 Special relationship between binary and hexadecimal, and binary and octal12m

2.201 Hidden messages inside an image21m

2.301 Arithmetic in hexadecimal/octal8m

2.303 Other bases9m

2.401 Summary1m

2.203 Task 3: Steganography – instructions15m

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

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

2.106 Translate between binary and hexadecimal/octal40m

2.302 Arithmetic in hexadecimal/octals

2.304 Other bases5m

2.401 Number Bases Summative Quizs

Week

3In 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 videos (Total 111 min), 3 readings, 10 quizzes

3.102 Computing n mod k13m

3.104 Addition mod k7m

3.106 Additive identity and inverse mod k8m

3.201 Multiplication mod k9m

3.204 Multiplicative identity, inverse mod k, exponentiation mod k31m

3.206 Mod, rem and division5m

3.301 Encryption using modular arithmetic20m

3.401 Summary4m

3.002 Instruction on the summative quiz

3.003 Modular Arithmetic Summative Quiz30m

3.302 Task 5: Encryption using modular arithmetic – instructions20m

3.101 Clock arithmetic5m

3.103 Computing n mod k15m

3.105 Addition mod k12m

3.108 Computing additive inverses mod k25m

3.203 Multiplication mod k15m

3.205 Computing multiplicative inverses mod k; exponentiation mod k30m

3.207 Use the operator ‘rem’10m

3.402 Modular Arithmetic Summative Quiz40m

Josephus problem30m

Week

4In 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 videos (Total 72 min), 6 readings, 5 quizzes

4.101 Introduction to sequences of numbers6m

4.103 Defining sequences17m

4.201 Arithmetic progressions8m

4.203 Geometric progressions12m

4.301 ISO Paper format7m

4.305 Task 7: Investigating random numbers8m

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

4.002 Instruction to the summative quiz

4.003 Sequences and Series Summative Quiz30m

4.004 Optional reading2m

4.302 Task 6: Investigating ISO paper format – instructions5m

4.307 Task 7: Generating random numbers – instructions10m

4.402 Sequences and Series Summative Quiz30m

4.102 Patterns in sequences10m

4.104 Defining sequences and terms5m

4.202 Working with arithmetic progressions20m

4.204 Geometric progressions; sequences15m

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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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