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

Part of the Bachelor of Science in Computer Science degree

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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!”

Course 3 of 3 in the

Introduction to Computer Science and Programming Specialization

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Flexible deadlines

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Beginner Level

Approx. 35 hours to complete

Suggested: 13 hours/week...

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.

Learners taking this Course are

Chief Technology Officers (CTOs)
Technical Solutions Engineers
Software Engineers

Data Engineers
Technical Support Associates

Course 3 of 3 in the

Introduction to Computer Science and Programming Specialization

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Beginner Level

Approx. 35 hours to complete

Suggested: 13 hours/week...

English

Subtitles: English

Syllabus - What you will learn from this course

Week

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.

13 videos (Total 137 min), 4 readings, 9 quizzes

13 videos

0.001 Overview of using Numerical Mathematics in Computing6m

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

Week

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.

7 videos (Total 78 min), 2 readings, 7 quizzes

7 videos

2.101 Octal and hexadecimal (integer)12m

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

Week

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.

9 videos (Total 111 min), 2 readings, 9 quizzes

9 videos

3.001 Introduction to modular arithmetic10m

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

Week

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.

7 videos (Total 65 min), 3 readings, 5 quizzes

7 videos

4.001 Introduction to sequences and series11m

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

Week

4 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 114 min), 1 reading, 8 quizzes

10 videos

5.101 Series: sums of terms of sequences; summation symbol: sigma notation25m

5.104 Finite sum of arithmetic sequences7m

5.106 Finite sum of geometric sequences12m

5.108 Finite sums4m

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 convergence53s

5.301 Summary of sequences and series3m

1 reading

5.100 Sequences and series summative quiz10m

8 practice exercises

5.103 Series: sums of terms of sequences; summation symbol: sigma notation20m

5.105 Finite sum of arithmetic sequences2m

5.107 Finite sum of geometric sequences5m

5.110 Finite sums6m

5.202 Limits of sequences4m

5.205 Limits of series6m

5.208 Criteria for identifying convergent/divergent sequences and series4m

5.302 Sequences and series summative quiz45m

Week

6 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.

17 videos (Total 131 min), 2 readings, 5 quizzes

17 videos

6.001 Introduction to graph sketching and kinematics2m

6.101 Cartesian coordinates16m

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 - cubics7m

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

2 readings

6.002 Graph sketching and kinematics summative quiz2m

6.003 Optional reading1h

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 quiz45m

Instructor

Dr Matthew Yee-King

Lecturer

Computing Department, Goldsmiths, University of London

Start working towards your Master's degree

This course is part of the 100% online Bachelor of Science in Computer Science from University of London. If you are admitted to the full program, your courses count towards your degree learning.

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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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