“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!”
Этот курс входит в специализацию ''Специализация Introduction to Computer Science and Programming'
Mathematics for Computer Science
от партнера
Лондонский университет
Голдсмитский колледж, Лондонский университет
Об этом курсе
3.8
Оценки: 10
Чему вы научитесь
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.
Программа курса: что вы изучите
Неделя
19 ч. на завершение
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 видео ((всего 137 мин.)), 6 материалов для самостоятельного изучения, 9 тестов
13 видео
1.001 Introduction to number bases and modular arithmetic17мин
1.101 Introduction to number bases17мин
1.103 Place value for integers: binary to decimal7мин
1.105 Place value for integers: decimal to binary4мин
1.107 Place value for fractional numbers: binary9мин
1.109 Rational and irrational numbers: decimal and binary20мин
1.114 Summary of binary system and getting ready for operations in binary53
1.201 Addition in binary4мин
1.203 Subtraction in binary5мин
1.205 Multiplication in binary6мин
1.208 Review of Tasks 1 and 235мин
1.210 Summary and context of binary in computing48
6 материала для самостоятельного изучения
Acknowledgements1мин
0.003 Technical requirements10мин
0.004 Optional reading1мин
1.003 Number Bases Summative Quiz
1.112 Task 1: Algorithm for translation between decimal and binary10мин
1.300 Number Bases Summative Quiz30мин
8 практического упражнения
1.102 Identifying number bases10мин
1.104 Integer binary to decimal20мин
1.106 Translating from decimal to binary (integers)20мин
1.108 Translating between decimal and binary fractional numbers15мин
1.110 Rational and irrational numbers: decimal and binary15мин
1.202 Addition in binary15мин
1.204 Subtraction in binary15мин
1.206 Multiplication in binary15мин
Неделя
28 ч. на завершение
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 видео ((всего 78 мин.)), 1 материал для самостоятельного изучения, 7 тестов
7 видео
2.103 Octal and hexadecimal (fractional)11мин
2.105 Special relationship between binary and hexadecimal, and binary and octal12мин
2.201 Hidden messages inside an image21мин
2.301 Arithmetic in hexadecimal/octal8мин
2.303 Other bases9мин
2.401 Summary1мин
1 материал для самостоятельного изучения
2.203 Task 3: Steganography – instructions15мин
6 практического упражнения
2.102 Translate between decimal and octal or hexadecimal (integer)40мин
2.104 Translate between decimal and hexadecimal or octal (fractional)20мин
2.106 Translate between binary and hexadecimal/octal40мин
2.302 Arithmetic in hexadecimal/octal
2.304 Other bases5мин
2.401 Number Bases Summative Quiz
Неделя
38 ч. на завершение
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 видео ((всего 111 мин.)), 3 материалов для самостоятельного изучения, 10 тестов
9 видео
3.102 Computing n mod k13мин
3.104 Addition mod k7мин
3.106 Additive identity and inverse mod k8мин
3.201 Multiplication mod k9мин
3.204 Multiplicative identity, inverse mod k, exponentiation mod k31мин
3.206 Mod, rem and division5мин
3.301 Encryption using modular arithmetic20мин
3.401 Summary4мин
3 материала для самостоятельного изучения
3.002 Instruction on the summative quiz
3.003 Modular Arithmetic Summative Quiz30мин
3.302 Task 5: Encryption using modular arithmetic – instructions20мин
9 практического упражнения
3.101 Clock arithmetic5мин
3.103 Computing n mod k15мин
3.105 Addition mod k12мин
3.108 Computing additive inverses mod k25мин
3.203 Multiplication mod k15мин
3.205 Computing multiplicative inverses mod k; exponentiation mod k30мин
3.207 Use the operator ‘rem’10мин
3.402 Modular Arithmetic Summative Quiz40мин
Josephus problem30мин
Неделя
45 ч. на завершение
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 видео ((всего 72 мин.)), 6 материалов для самостоятельного изучения, 5 тестов
8 видео
4.101 Introduction to sequences of numbers6мин
4.103 Defining sequences17мин
4.201 Arithmetic progressions8мин
4.203 Geometric progressions12мин
4.301 ISO Paper format7мин
4.305 Task 7: Investigating random numbers8мин
4.401 Summary of Sequences and preparation for next week.1мин
6 материала для самостоятельного изучения
4.002 Instruction to the summative quiz
4.003 Sequences and Series Summative Quiz30мин
4.004 Optional reading2мин
4.302 Task 6: Investigating ISO paper format – instructions5мин
4.307 Task 7: Generating random numbers – instructions10мин
4.402 Sequences and Series Summative Quiz30мин
4 практического упражнения
4.102 Patterns in sequences10мин
4.104 Defining sequences and terms5мин
4.202 Working with arithmetic progressions20мин
4.204 Geometric progressions; sequences15мин
Преподаватели
Dr Matthew Yee-King
LecturerComputing Department, Goldsmiths, University of London
Dr Sara Santos
Lecturer of MathematicsComputing Department, Goldsmiths, University of London
О Лондонский университет
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
О Голдсмитский колледж, Лондонский университет
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.
О специализации ''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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