University of Surrey (UNIS)

Lecture notes for the module 'MAT2048 Groups and Rings' in the Mathematics course. Topics covered in the notes include: - Binary Operations, Magmas, Semi Group, Monoid - Finite Groups and Cayley Tables - Permutations and Symmetries - Subgroups - Cosets and Lagrange Theorem - Group Homomorphisms - Normal Subgroups and Quotient Group - Rings and Fields - Homomorphisms, Ideals and Quotient Rings Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT 3043 Graphs and Networks' in the Mathematics course. Topics covered in the notes include: - Graphs - Connectedness - Eulerian and Hamiltonian Graphs - Trees - Planar Graphs and Geometric Dual - Graph Colourings - Matchings and Networks Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT3004 Introduction to Function Spaces' in the Mathematics course. Topics covered in the notes include: - Metric Spaces - Normed Spaces - Continuity and Convergence - Open and Closed Sets Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT3040 Mathematical Ecology and Epidemiology' in the Mathematics course. Topics covered in the notes include: - Single Species Ecology - Harvesting and Fishing - Interacting Species Populations - Predator-Prey Models - Competition and Mutualism Modelling - SIR and SEI Models - Quarantining - Spatial Ecology Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT2047 Curves and Surfaces' in the Mathematics course. Topics covered in the notes include: - Vectors and Matrices - Isometric Transformation - Exponentiation - Plane Curves - Frenet-Serret Frame - Curvature - Rotation Number - Fundamental Forms Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT1036 Classical Dynamics'. Topics covered in the notes include: - Reference Frames - Displacement and Vectors - Velocity and Acceleration - Mass, Momentum and Forces - Newtons Laws - Gravity - Work and Energy - Systems of Particles - Angular Motion Definitions in pink, formulae and equations in green, examples in blue.

Lecture Notes for the module 'MAT1031 Algebra'. Topics covered in the notes include: - Basics such as proofs, sets, polynomials, divisibility and more - Vectors - Permutations and Cross Product - Groups and Fields Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'Advanced Algebra'. Topics covered in the notes include: - Groups - Generators and presentations - Cosets, Products and Quotient Groups - Abelian Groups, Automorphisms and Semi-Direct Products - Groups Actions - Conjugacy in Groups Definitions in pink, formulae and equations in green, examples in blue.

In-depth coverage of all Software Engineering concepts. Requirements engineering, user vs system requirements, functional hierarchies, documentation, testing and design life cycles. User understanding, features, personas and scenarios, actors, user stories, feature creep and lists. Product-based engineering notes and differences, prototyping, waterfall and agile models, extreme programming, test-first principles, incemental development. Scrum and sprints in agile development, backlog management,...

In-depth coverage going over mathematics for computer scientists. Probability, permutations, bionomial and pascals triangle. Axioms, logic and proofs, regular languages and finite automata, sets and venn diagrams and their relationships. In depth coverage of number theory. Strings, concatenation and formal languages. Regular expressions, DFAs, NFAs, Kleene's Theorem, atomic and compound syntax rules. Automata construction in detail, truth tables and boolean algebra, basic natural language proce...