John Hopkins University - Mathematics for Computer Science 

0.001 Overview of using Numerical Mathematics in Computing

1.001 Introduction to number bases and modular arithmetic

1.101 Introduction to number bases

1.103 Place value for integers: binary to decimal

1.105 Place value for integers: decimal to binary

1.107 Place value for fractional numbers: binary

1.109 Rational and irrational numbers: decimal and binary

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

1.201 Addition in binary

1.203 Subtraction in binary

1.205 Multiplication in binary

1.208 Review of Tasks

1.210 Summary and context of binary in computing

Acknowledgements

0.003 Technical requirements

0.004 Optional reading

1.003 Number bases summative quiz

1.102 Identifying number bases

1.104 Integer binary to decimal

1.106 Translating from decimal to binary (integers)

1.108 Translating between decimal and binary fractional numbers

1.110 Rational and irrational numbers: decimal and binary

1.202 Addition in binary

1.204 Subtraction in binary

1.206 Multiplication in binary

1.301 Binary (Number bases) summative quiz

Number bases - other bases

2.101 Octal and hexadecimal (integer)

2.103 Octal and hexadecimal (fractional)

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

2.201 Hidden messages inside an image

2.301 Arithmetic in hexadecimal/octal

2.303 Other bases

2.401 Summary

2.100 Number bases summative quiz

2.203 Task: Steganography ? instructions

2.102 Translate between decimal and octal or hexadecimal (integer)

2.104 Translate between decimal and hexadecimal or octal (fractional)

2.106 Translate between binary and hexadecimal/octal

2.302 Arithmetic in hexadecimal/octal

2.304 Other bases

2.402 Number bases summative quiz

Modular arithmetic

3.001 Introduction to modular arithmetic

3.102 Computing n mod k

3.104 Addition mod k

3.106 Additive identity and inverse mod k

3.201 Multiplication mod k

3.204 Multiplicative identity, inverse mod k, exponentiation mod k

3.206 Mod, rem and division

3.401 Summary

3.301 Encryption using modular arithmetic

3.002 Modular arithmetic summative quiz

3.302 Task: Encryption using modular arithmetic ? instructions

3.101 Clock arithmetic

3.103 Computing n mod k

3.105 Addition mod k

3.108 Computing additive inverses mod k

3.203 Multiplication mod k

3.205 Computing multiplicative inverses mod k; exponentiation mod k

3.207 Use the operator ?rem?

3.402 Modular arithmetic summative quiz

Sequences

4.001 Introduction to sequences and series

4.101 Introduction to sequences of numbers

4.103 Defining sequences

4.201 Arithmetic progressions

4.203 Geometric progressions

4.305 Task: Investigating random numbers

4.401 Summary of sequences and preparation for next week

4.002 Sequences and series summative quiz

4.003 Optional reading

4.307 Task: Generating random numbers ? instructions

4.102 Patterns in sequences

4.104 Defining sequences and terms

4.202 Working with arithmetic progressions

4.204 Geometric progressions; sequences

4.402 Sequences and series summative quiz

Series

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

5.104 Finite sum of arithmetic sequences

5.106 Finite sum of geometric sequences

5.108 Finite sums

5.111 Summary of series; infinite sequences and sums

5.201 Patterns in infinite sequences; limit; convergence and divergence

5.204 Patterns in series; limit; convergent and divergent series

5.206 Criteria for identifying convergent/ divergent sequence and series

5.209 Summary of convergence

5.301 Summary of sequences and series

5.100 Sequences and series summative quiz

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

5.105 Finite sum of arithmetic sequences

5.107 Finite sum of geometric sequences

5.110 Finite sums

5.202 Limits of sequences

5.205 Limits of series

5.208 Criteria for identifying convergent/divergent sequences and series

5.302 Sequences and series summative quiz

Introduction to Graph Sketching and Kinematics

6.001 Introduction to graph sketching and kinematics

6.101 Cartesian coordinates

6.201 Introduction to functions and graphs

6.204 Functions and tables of values

6.206 Plotting graphs by hand - aspects to consider

6.207 Plotting graphs by hand ? straight lines

6.208 Plotting graphs by hand - quadratics

6.209 Plotting graphs by hand - cubics

6.210 Plotting graphs by hand ? higher order polynomials

6.211 Plotting graphs by hand ? reciprocal

6.212 Plotting graphs by hand ? rational functions

6.213 Plotting graphs by hand - piecewise

6.301 Transformations of graphs

6.307 Summary of graphs

6.401 Kinematic equations

6.403 Summary of kinematics

6.501 Summary

6.002 Graph sketching and kinematics summative quiz

6.003 Optional reading

6.104 Cartesian coordinates and conditions

6.205 Graphs and tables of values

6.302 Transformations of graphs

6.402 Kinematic equations

6.502 Graphs of functions and kinematics summative quiz