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MA12010: Core pure and applied 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%)
  • Multivariable calculus & differential equations 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).
  • Visualise curves, surfaces and solids and formulate their mathematical descriptions; interpret and work with partial derivatives and multiple integrals; and interpret, construct, and solve standard first-order and second-order linear differential equations.
  • 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 explore calculus in two and three dimensions and key mathematical methods for solving linear differential equations. Mathematical methods will be motivated with examples from physics, engineering and other sciences.

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. Multivariable calculus & differential equations: Visualisation and analysis of space in rectangular, polar, cylindrical and spherical co-ordinate systems, arc length, surfaces of revolution. Visualisation and parameterisation of three-dimensional surfaces (planes, paraboloids, spheres, cylinders, cones). Partial derivatives, critical points, chain rule. Jacobians and change of variables, double integrals over rectangular and non-rectangular domains, triple integrals, surface area and volume, the Riemann interpretation. Key applications. Dynamics and differential equations: first-order linear and nonlinear differential equations, integrating factors, separable equations. Review of complex numbers and Euler's formula. Second-order linear constant-coefficient equations: characteristic equations, real and complex roots, general real solutions, inhomogeneous problems. Key applications. Sequences: Logic, quantifiers. Numbers and inequalities. Sequences. Series. Limits

Course availability:

MA12010 is Compulsory on the following courses:

Department of Mathematical Sciences
  • USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 1)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 1)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 1)
Department of Physics
  • USPH-AFB26 : BSc(Hons) Mathematics and Physics (Year 1)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with professional placement (Year 1)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with study abroad (Year 1)
  • USPH-AFM26 : MSci(Hons) Mathematics and Physics (Year 1)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with professional placement (Year 1)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics 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.