- Academic Registry
Course & Unit Catalogues


MA12001: Pure mathematics 1A

[Page last updated: 23 October 2023]

Academic Year: 2023/24
Owning Department/School: Department of Mathematical Sciences
Credits: 15 [equivalent to 30 CATS credits]
Notional Study Hours: 300
Level: Certificate (FHEQ level 4)
Period:
Semester 1
Assessment Summary: CWRG 20%, EXCB 80%
Assessment Detail:
  • Analysis 1a (EXCB 40%)
  • Algebra 1a (EXCB 40%)
  • Foundations (CWRG 20%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Learning Outcomes: After taking this unit, you will be able to:
  • Demonstrate understanding of sequences and series, including the construction of proofs.
  • Demonstrate understanding of the elementary concepts of geometry and algebra, including the construction of proofs and computations with numbers, polynomials, and matrices (e.g., the solution of systems of linear equations).
  • Read and manipulate logical statements about mathematical objects, determine the validity of mathematical arguments, and formulate and write mathematical proofs using construction, contradiction, and induction.



Synopsis: You will develop core skills in pure mathematics. You will study algebra and build a firm grounding in the fundamental objects of mathematics such as sets, functions, numbers, polynomials and matrices. You will study analysis to define the notions of convergence and limit precisely. You will also develop the ability to reason logically and to read and write mathematics well.

Content: Analysis: Logic, quantifiers, real and complex numbers, order, absolute value, triangle and reverse triangle inequalities. Sequences: convergence, uniqueness, algebra of limits, monotone sequences, tests for convergence, subsequences, Cauchy sequences, limsup and liminf. Countability. Series: definition and convergence, series of non- negative terms, absolute convergence, alternating series, tests for convergence, multiplying series. Algebra: Sets and functions: constructions and properties, cardinality. Equivalence relations and partitions. Permutations: cycle notation and sign, the symmetric group. Numbers (natural, integer, rational, real, complex); algebraic properties as rings and fields. Primes, factorisation and Euclid's algorithm; modular arithmetic. The complex plane: complex exponentials, roots of unity. Polynomials: division with remainder, coprime polynomials. Matrices with real coefficients: matrix algebra, linear transformations, 2-by-2 and 3-by-3 determinants, geometric interpretation. Systems of linear equations: matrix representation, row operations and row echelon form. Foundations: Study skills for mathematicians, including how to think and write logically, how to work with definitions, theorems and proofs, and techniques of proof, including construction, contradiction, and induction.

Course availability:

MA12001 is Compulsory on the following courses:

Department of Mathematical Sciences
  • USMA-AFB30 : BSc(Hons) Mathematics (Year 1)
  • USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 1)
  • USMA-AKB32 : BSc(Hons) Mathematics and Statistics with professional placement (Year 1)
  • USMA-AKB32 : BSc(Hons) Mathematics and Statistics with study abroad (Year 1)
  • USMA-AKB30 : BSc(Hons) Mathematics with professional placement (Year 1)
  • USMA-AKB30 : BSc(Hons) Mathematics with study abroad (Year 1)
  • USMA-AFM30 : MMath(Hons) Mathematics (Year 1)
  • USMA-AKM30 : MMath(Hons) Mathematics with professional placement (Year 1)
  • USMA-AKM31 : MMath(Hons) Mathematics with study abroad (Year 1)

Notes:

  • This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24.
  • Courses and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
  • Find out more about these and other important University terms and conditions here.