MA24110 Combinatorics
Introductory description
N/A
Module aims
N/A
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
I Enumerative combinatorics
Basic counting (Lists with and without repetitions, Binomial coefficients and the Binomial Theorem)
Applications of the Binomial Theorem (Multinomial Theorem, Multiset formula, Principle of inclusion/exclusion)
Linear recurrence relations and the Fibonacci numbers
Generating functions and the Catalan numbers
Permutations, Partitions and the Stirling and Bell numbers
II Graph Theory
Basic concepts (isomorphism, connectivity, Euler circuits)
Trees (basic properties of trees, spanning trees, counting trees)
Planarity (Euler's formula, Kuratowski’s theorem, the Four Colour Problem)
Matching Theory (Hall's Theorem and Systems of Distinct Representatives)
Elements of Ramsey Theory
III Boolean Functions
Learning outcomes
By the end of the module, students should be able to:
 N/A
Indicative reading list
Edward E. Bender and S. Gill Williamson, Foundations of Combinatorics with Applications, Dover Publications, 2006. Available online at the author's website: http://www.math.ucsd.edu/~ebender/CombText/
John M. Harris, Jeffry L. Hirst and Michael J. Mossinghoff, Combinatorics and graph theory, SpringerVerlag, 2000.
Subject specific skills
N/A
Transferable skills
Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.
Study time
Type  Required 

Lectures  20 sessions of 1 hour (20%) 
Tutorials  9 sessions of 1 hour (9%) 
Private study  71 hours (71%) 
Total  100 hours 
Private study description
Review lectured material and work on set exercises.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D
Weighting  Study time  

Assignments  10%  
4 fortnightly assignments during the term. 

Examination  90%  

Assessment group R
Weighting  Study time  

Inperson Examination  Resit  100%  

Feedback on assessment
Marked assignments and exam feedback.
Courses
This module is Core for:

UCSAG4G1 Undergraduate Discrete Mathematics
 Year 2 of G4G1 Discrete Mathematics
 Year 2 of G4G1 Discrete Mathematics
 Year 2 of UCSAG4G3 Undergraduate Discrete Mathematics
This module is Optional for:
 Year 2 of UCSAI1N1 Undergraduate Computer Science with Business Studies
This module is Core option list A for:

UMAAGV17 Undergraduate Mathematics and Philosophy
 Year 2 of GV17 Mathematics and Philosophy
 Year 2 of GV17 Mathematics and Philosophy
 Year 2 of GV17 Mathematics and Philosophy
 Year 2 of UMAAGV19 Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations
This module is Core option list B for:
 Year 3 of UMAAGV19 Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations
This module is Core option list D for:
 Year 4 of UMAAGV19 Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations
This module is Option list A for:

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 2 of G105 Mathematics (MMath) with Intercalated Year
 Year 4 of G105 Mathematics (MMath) with Intercalated Year

UMAAG100 Undergraduate Mathematics (BSc)
 Year 2 of G100 Mathematics
 Year 2 of G100 Mathematics
 Year 2 of G100 Mathematics
 Year 3 of G100 Mathematics
 Year 3 of G100 Mathematics
 Year 3 of G100 Mathematics

UMAAG103 Undergraduate Mathematics (MMath)
 Year 2 of G100 Mathematics
 Year 2 of G103 Mathematics (MMath)
 Year 2 of G103 Mathematics (MMath)
 Year 3 of G100 Mathematics
 Year 3 of G103 Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 2 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 2 of UMAAG1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
 Year 2 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 2 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 2 of GG14 Mathematics and Statistics
 Year 2 of GG14 Mathematics and Statistics

UMAAG101 Undergraduate Mathematics with Intercalated Year
 Year 2 of G101 Mathematics with Intercalated Year
 Year 4 of G101 Mathematics with Intercalated Year
This module is Option list B for:

UCSAG500 Undergraduate Computer Science
 Year 2 of G500 Computer Science
 Year 2 of G500 Computer Science

UCSAG503 Undergraduate Computer Science MEng
 Year 2 of G500 Computer Science
 Year 2 of G503 Computer Science MEng
 Year 2 of G503 Computer Science MEng

USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 2 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 2 of Y602 Mathematics,Operational Research,Stats,Economics