“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.
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 SpecializationUniversity of LondonAbout this Course
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Beginner Level
Approx. 36 hours to complete
English
Subtitles: English
What you will learn
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.
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Course 3 of 3 in the
Flexible deadlines
Reset deadlines in accordance to your schedule.
Beginner Level
Approx. 36 hours to complete
English
Subtitles: English
Offered by
University of London
The University of London is a federal University which includes 18 world leading Colleges. Our distance learning programmes were founded in 1858 and have enriched the lives of thousands of students, delivering high quality University of London degrees wherever our students are across the globe. Our alumni include 7 Nobel Prize winners. Today, we are a global leader in distance and flexible study, offering degree programmes to over 50,000 students in over 180 countries. To find out more about studying for one of our degrees where you are, visit www.london.ac.uk
Goldsmiths, University of London
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.
Syllabus - What you will learn from this course
6 hours to complete
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.
6 hours to complete
13 videos (Total 137 min), 4 readings, 9 quizzes
13 videos
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 Tasks35m
1.210 Summary and context of binary in computing48s
4 readings
Acknowledgements1m
0.003 Technical requirements10m
0.004 Optional reading10m
1.003 Number bases summative quiz10m
9 practice exercises
1.102 Identifying number bases15m
1.104 Integer binary to decimal20m
1.106 Translating from decimal to binary (integers)8m
1.108 Translating between decimal and binary fractional numbers15m
1.110 Rational and irrational numbers: decimal and binary 8m
1.202 Addition in binary2m
1.204 Subtraction in binary3m
1.206 Multiplication in binary6m
1.301 Binary (Number bases) summative quiz45m
8 hours to complete
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.
8 hours to complete
7 videos (Total 78 min), 2 readings, 7 quizzes
7 videos
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/octal9m
2.303 Other bases9m
2.401 Summary1m
2 readings
2.100 Number bases summative quiz10m
2.203 Task: Steganography – instructions20m
6 practice exercises
2.102 Translate between decimal and octal or hexadecimal (integer)40m
2.104 Translate between decimal and hexadecimal or octal (fractional)30m
2.106 Translate between binary and hexadecimal/octal30m
2.302 Arithmetic in hexadecimal/octal30m
2.304 Other bases10m
2.402 Number bases summative quiz45m
8 hours to complete
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.
8 hours to complete
9 videos (Total 111 min), 2 readings, 9 quizzes
9 videos
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
3.401 Summary4m
3.301 Encryption using modular arithmetic20m
2 readings
3.002 Modular arithmetic summative quiz10m
3.302 Task: Encryption using modular arithmetic – instructions20m
8 practice exercises
3.101 Clock arithmetic30m
3.103 Computing n mod k6m
3.105 Addition mod k30m
3.108 Computing additive inverses mod k10m
3.203 Multiplication mod k6m
3.205 Computing multiplicative inverses mod k; exponentiation mod k12m
3.207 Use the operator ‘rem’2m
3.402 Modular arithmetic summative quiz45m
4 hours to complete
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.
4 hours to complete
7 videos (Total 65 min), 3 readings, 5 quizzes
7 videos
4.101 Introduction to sequences of numbers6m
4.103 Defining sequences17m
4.201 Arithmetic progressions8m
4.203 Geometric progressions11m
4.305 Task: Investigating random numbers8m
4.401 Summary of sequences and preparation for next week59s
3 readings
4.002 Sequences and series summative quiz30m
4.003 Optional reading30m
4.307 Task: Generating random numbers – instructions20m
5 practice exercises
4.102 Patterns in sequences4m
4.104 Defining sequences and terms2m
4.202 Working with arithmetic progressions4m
4.204 Geometric progressions; sequences4m
4.402 Sequences and series summative quiz45m
About the Introduction to Computer Science and Programming Specialization
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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