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MA12012: Core pure and statistical mathematics A

[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: EXCB 100%
Assessment Detail:
  • Algebra 1a exam (EXCB 40%)
  • Probability & Statistics 1a (EXCB 40%)
  • Sequences (EXCB 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 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).
  • Apply the axioms and laws of probability to solve a variety of problems, including the use of combinations, permutations, and standard probability distributions.
  • Demonstrate fluency and familiarity with elementary definitions and results concerning sequence and series and apply these concepts to a range of examples.



Synopsis: You will develop core skills in 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. You will develop a solid foundation in probability theory that will facilitate further study in probability and statistics.

Content: 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. Probability & Statistics: Sample space, events as sets, unions, and intersections. Axioms and laws of probability. Equally likely events. Sampling methods: with or without ordering and replacement. Conditional probability. Partition theorem. Bayes' theorem. Independence of events. Bernoulli trials. Discrete random variables (RVs). Probability mass function (PMF). Bernoulli, Geometric, Binomial and Poisson distributions. Joint and marginal discrete distributions. Definition of continuous random variables (RVs), cumulative distribution functions (CDFs) and probability density functions (PDFs). Some common continuous distributions including uniform, exponential and normal. Independence of RVs (including joint distribution as a product of marginals). Expectation of RVs. Properties of expectation. Expectation of product of independent RVs. Variance and properties. Standard deviation. Moments, covariance, correlation. Sums of independent random variables. Key application: Random walks. Statement of the law of large numbers. Sequences: Logic, quantifiers. Numbers and inequalities. Sequences. Series. Limits

Course availability:

MA12012 is Compulsory on the following courses:

Department of Computer Science
  • USCM-AFB32 : BSc(Hons) Computer Science and Mathematics (Year 1)
  • USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with professional placement (Year 1)
  • USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with study abroad (Year 1)
  • USCM-AFM32 : MComp(Hons) Computer Science and Mathematics (Year 1)
  • USCM-AKM32 : MComp(Hons) Computer Science and Mathematics with professional placement (Year 1)
  • USCM-AKM32 : MComp(Hons) Computer Science and Mathematics with study abroad (Year 1)
Department of Economics
  • UHES-AFB12 : BSc(Hons) Economics and Mathematics (Year 1)
  • UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement (Year 1)
  • UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement and study abroad (Year 1)
  • UHES-AKB12 : BSc(Hons) Economics and 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.