Este curso faz parte do Programa de cursos integrados Introduction to Computer Science and Programming

Mathematics for Computer Science

oferecido por

Universidade de Londres

Goldsmiths, University of London

Programa de cursos integrados Introduction to Computer Science and Programming

Universidade de Londres

Informações sobre o curso

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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!”

Learner Career Outcomes

Curso 3 de 3 no

Programa de cursos integrados Introduction to Computer Science and Programming

100% on-line

Comece imediatamente e aprenda em seu próprio cronograma.

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Nível iniciante

Aprox. 39 horas para completar

Sugerido: 13 hours/week...

Inglês

Legendas: Inglês

O que você vai aprender

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.

Learner Career Outcomes

Curso 3 de 3 no

Programa de cursos integrados Introduction to Computer Science and Programming

100% on-line

Comece imediatamente e aprenda em seu próprio cronograma.

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Nível iniciante

Aprox. 39 horas para completar

Sugerido: 13 hours/week...

Inglês

Legendas: Inglês

Programa - O que você aprenderá com este curso

Semana

6 horas para concluir

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 vídeos (Total 137 mín.), 4 leituras, 9 testes

13 videos

0.001 Overview of using Numerical Mathematics in Computing6min

1.001 Introduction to number bases and modular arithmetic17min

1.101 Introduction to number bases17min

1.103 Place value for integers: binary to decimal7min

1.105 Place value for integers: decimal to binary4min

1.107 Place value for fractional numbers: binary9min

1.109 Rational and irrational numbers: decimal and binary20min

1.114 Summary of binary system and getting ready for operations in binary53s

1.201 Addition in binary4min

1.203 Subtraction in binary5min

1.205 Multiplication in binary6min

1.208 Review of Tasks35min

1.210 Summary and context of binary in computing48s

4 leituras

Acknowledgements1min

0.003 Technical requirements10min

0.004 Optional reading10min

1.003 Number bases summative quiz10min

9 exercícios práticos

1.102 Identifying number bases15min

1.104 Integer binary to decimal20min

1.106 Translating from decimal to binary (integers)8min

1.108 Translating between decimal and binary fractional numbers15min

1.110 Rational and irrational numbers: decimal and binary 8min

1.202 Addition in binary2min

1.204 Subtraction in binary3min

1.206 Multiplication in binary6min

1.301 Binary (Number bases) summative quiz45min

Semana

8 horas para concluir

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 vídeos (Total 78 mín.), 2 leituras, 7 testes

7 videos

2.101 Octal and hexadecimal (integer)12min

2.103 Octal and hexadecimal (fractional)11min

2.105 Special relationship between binary and hexadecimal, and binary and octal12min

2.201 Hidden messages inside an image21min

2.301 Arithmetic in hexadecimal/octal9min

2.303 Other bases9min

2.401 Summary1min

2 leituras

2.100 Number bases summative quiz10min

2.203 Task: Steganography – instructions20min

6 exercícios práticos

2.102 Translate between decimal and octal or hexadecimal (integer)40min

2.104 Translate between decimal and hexadecimal or octal (fractional)30min

2.106 Translate between binary and hexadecimal/octal30min

2.302 Arithmetic in hexadecimal/octal30min

2.304 Other bases10min

2.402 Number bases summative quiz45min

Semana

8 horas para concluir

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 vídeos (Total 111 mín.), 2 leituras, 9 testes

9 videos

3.001 Introduction to modular arithmetic10min

3.102 Computing n mod k13min

3.104 Addition mod k7min

3.106 Additive identity and inverse mod k8min

3.201 Multiplication mod k9min

3.204 Multiplicative identity, inverse mod k, exponentiation mod k31min

3.206 Mod, rem and division5min

3.401 Summary4min

3.301 Encryption using modular arithmetic20min

2 leituras

3.002 Modular arithmetic summative quiz10min

3.302 Task: Encryption using modular arithmetic – instructions20min

8 exercícios práticos

3.101 Clock arithmetic30min

3.103 Computing n mod k6min

3.105 Addition mod k30min

3.108 Computing additive inverses mod k10min

3.203 Multiplication mod k6min

3.205 Computing multiplicative inverses mod k; exponentiation mod k12min

3.207 Use the operator ‘rem’2min

3.402 Modular arithmetic summative quiz45min

Semana

4 horas para concluir

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 vídeos (Total 65 mín.), 3 leituras, 5 testes

7 videos

4.001 Introduction to sequences and series11min

4.101 Introduction to sequences of numbers6min

4.103 Defining sequences17min

4.201 Arithmetic progressions8min

4.203 Geometric progressions11min

4.305 Task: Investigating random numbers8min

4.401 Summary of sequences and preparation for next week59s

3 leituras

4.002 Sequences and series summative quiz30min

4.003 Optional reading30min

4.307 Task: Generating random numbers – instructions20min

5 exercícios práticos

4.102 Patterns in sequences4min

4.104 Defining sequences and terms2min

4.202 Working with arithmetic progressions4min

4.204 Geometric progressions; sequences4min

4.402 Sequences and series summative quiz45min

Semana

4 horas para concluir

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 vídeos (Total 114 mín.), 1 leitura, 8 testes

10 videos

5.101 Series: sums of terms of sequences; summation symbol: sigma notation25min

5.104 Finite sum of arithmetic sequences7min

5.106 Finite sum of geometric sequences12min

5.108 Finite sums4min

5.111 Summary of series; infinite sequences and sums1min

5.201 Patterns in infinite sequences; limit; convergence and divergence22min

5.204 Patterns in series; limit; convergent and divergent series21min

5.206 Criteria for identifying convergent/ divergent sequence and series14min

5.209 Summary of convergence53s

5.301 Summary of sequences and series3min

1 leituras

5.100 Sequences and series summative quiz10min

8 exercícios práticos

5.103 Series: sums of terms of sequences; summation symbol: sigma notation20min

5.105 Finite sum of arithmetic sequences2min

5.107 Finite sum of geometric sequences5min

5.110 Finite sums6min

5.202 Limits of sequences4min

5.205 Limits of series6min

5.208 Criteria for identifying convergent/divergent sequences and series4min

5.302 Sequences and series summative quiz45min

Semana

6 horas para concluir

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 vídeos (Total 131 mín.), 2 leituras, 5 testes

17 videos

6.001 Introduction to graph sketching and kinematics2min

6.101 Cartesian coordinates16min

6.201 Introduction to functions and graphs4min

6.204 Functions and tables of values16min

6.206 Plotting graphs by hand - aspects to consider2min

6.207 Plotting graphs by hand – straight lines5min

6.208 Plotting graphs by hand - quadratics10min

6.209 Plotting graphs by hand - cubics7min

6.210 Plotting graphs by hand – higher order polynomials4min

6.211 Plotting graphs by hand – reciprocal8min

6.212 Plotting graphs by hand – rational functions4min

6.213 Plotting graphs by hand - piecewise3min

6.301 Transformations of graphs26min

6.307 Summary of graphs1min

6.401 Kinematic equations13min

6.403 Summary of kinematics1min

6.501 Summary2min

2 leituras

6.002 Graph sketching and kinematics summative quiz2min

6.003 Optional reading1h

5 exercícios práticos

6.104 Cartesian coordinates and conditions15min

6.205 Graphs and tables of values15min

6.302 Transformations of graphs15min

6.402 Kinematic equations15min

6.502 Graphs of functions and kinematics summative quiz45min

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Instrutores

Dr Matthew Yee-King

Lecturer

Computing Department, Goldsmiths, University of London

Sobre Universidade 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...

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Sobre Programa de cursos integrados 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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