“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!”
This course is part of the Introduction to Computer Science and Programming Specialization
Mathematics for Computer Science
Offered By
University of London
Goldsmiths, University of London
2,822 enrolled
About this Course
24,087 recent views
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.
Syllabus - What you will learn from this course
Week
19 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.
13 videos (Total 137 min), 6 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 Tasks 1 and 235m
1.210 Summary and context of binary in computing48s
6 readings
Acknowledgements1m
0.003 Technical requirements10m
0.004 Optional reading1m
1.003 Number Bases Summative Quizs
1.112 Task 1: Algorithm for translation between decimal and binary10m
1.300 Number Bases Summative Quiz30m
8 practice exercises
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
28 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.
7 videos (Total 78 min), 1 reading, 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/octal8m
2.303 Other bases9m
2.401 Summary1m
1 reading
2.203 Task 3: Steganography – instructions15m
6 practice exercises
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
38 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.
9 videos (Total 111 min), 3 readings, 10 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
3.301 Encryption using modular arithmetic20m
3.401 Summary4m
3 readings
3.002 Instruction on the summative quiz
3.003 Modular Arithmetic Summative Quiz30m
3.302 Task 5: Encryption using modular arithmetic – instructions20m
9 practice exercises
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
45 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.
8 videos (Total 72 min), 6 readings, 5 quizzes
8 videos
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
6 readings
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 practice exercises
4.102 Patterns in sequences10m
4.104 Defining sequences and terms5m
4.202 Working with arithmetic progressions20m
4.204 Geometric progressions; sequences15m
Week
55 hours to complete
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 videos (Total 121 min), 8 quizzes
10 videos
5.104 Finite sum of arithmetic sequences7m
5.106 Finite sum of geometric sequences12m
5.108 Finite sums10m
5.111 Summary of series; infinite sequences and sums1m
5.201 Patterns in infinite sequences; limit; convergence and divergence22m
5.204 Patterns in series; limit; convergent and divergent series21m
5.206 Criteria for identifying convergent/ divergent sequence and series14m
5.209 Summary of Convergence1m
5.301 Summary of Sequences and Series3m
8 practice exercises
5.103 Series: sums of terms of sequences; summation symbol: sigma notation20m
5.105 Finite sum of arithmetic sequences5m
5.107 Finite sum of geometric sequences10m
5.110 Finite sums10m
5.202 Limits of sequences10m
5.205 Limits of series15m
5.208 Criteria for identifying convergent/divergent sequences and series10m
5.302 Sequences and Series Summative Quizs
Week
610 hours to complete
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 videos (Total 149 min), 6 readings, 7 quizzes
18 videos
6.101 Cartesian coordinates16m
6.105 Spiral15m
6.201 Introduction to functions and graphs4m
6.204 Functions and tables of values16m
6.206 Plotting graphs by hand - aspects to consider2m
6.207 Plotting graphs by hand – straight lines5m
6.208 Plotting graphs by hand - quadratics10m
6.209 Plotting graphs by hand - cubics8m
6.210 Plotting graphs by hand – higher order polynomials4m
6.211 Plotting graphs by hand – reciprocal8m
6.212 Plotting graphs by hand – rational functions4m
6.213 Plotting graphs by hand - piecewise3m
6.301 Transformations of graphs26m
6.307 Summary of graphs1m
6.401 Kinematic equations13m
6.403 Summary of kinematics1m
6.501 Summary2m
6 readings
6.002 Instruction on the summative quiz
6.003 Graph Sketching and Kinematics Summative Quiz30m
6.004 Optional reading
6.106 Task 8: Spiral: Instructions10m
6.214 Instructions for Task 10: graph plotting and sketching by hand10m
6.305 Instruction for Task 11: grouping functions using transformations of graphs10m
5 practice exercises
6.104 Cartesian coordinates and conditions15m
6.205 Graphs and tables of values15m
6.302 Transformations of graphs15m
6.402 Kinematic equations15m
6.502 Graphs of Functions and Kinematics Summative Quizs
Instructors
Dr Matthew Yee-King
LecturerComputing Department, Goldsmiths, University of London
Dr Sara Santos
Lecturer of MathematicsComputing Department, Goldsmiths, University of London
About 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
About 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.
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.
Frequently Asked Questions
When will I have access to the lectures and assignments?
Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.
What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
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Is financial aid available?
More questions? Visit the Learner Help Center.
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