“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!”
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
À propos de ce cours
3.8
10 notes
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.
Programme du cours : ce que vous apprendrez dans ce cours
Semaine
19 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
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 Quizs
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
28 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
2.103 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 lecture
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/octals
2.304 Other bases5 min
2.401 Number Bases Summative Quizs
Semaine
38 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
3.102 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
45 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
4.101 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
Enseignants
Dr Matthew Yee-King
LecturerComputing Department, Goldsmiths, University of London
Dr Sara Santos
Lecturer of MathematicsComputing Department, Goldsmiths, University of London
À propos de Université de Londres
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
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.
Foire Aux Questions
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