Mathematics for Computer Science

“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!”

• 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.
• 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.
• 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.
• 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.
• 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.
• 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.