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MA12004: Pure mathematics 1B

[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 2
Assessment Summary: CWOG 20%, EXCB 80%
Assessment Detail:
  • Analysis 1b (EXCB 40%)
  • Algebra 1b (EXCB 40%)
  • Connections coursework (CWOG 20%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA12001
Learning Outcomes: After taking this unit, you will be able to:
  • Demonstrate understanding of functions of one real variable, including the construction of proofs.
  • Demonstrate understanding of linear algebra, including bases, dimension, rank, orthogonality, diagonalisation, including proofs. Perform computations with determinants, matrix inverses, orthonormal bases, eigenvalues, and eigenvectors.
  • Discuss the breadth and importance of modern mathematical research.



Synopsis: You will develop further skills in pure mathematics. You will study linear algebra, both via matrices and via vector spaces and linear maps, focussing on the most widely applicable aspects. You will examine the theory of continuity, differentiation and integration for functions of one real variable. You will explore the beauty and the importance of university-level mathematics.

Content: Analysis: Limits of functions: uniqueness, algebra of limits. Continuity. Inertia principle. Weierstrass's theorem. Derivatives, rules of differentiation. Rolle's theorem. Mean-value theorem. Monotonicity. Maxima and minima. L'Hopital's rule. Taylor's theorem. Complex limits. Power series: exponential function, Euler's formula, trigonometric functions, differentiability. Algebra: Vector spaces (over the rational, real, and complex numbers), linear maps, subspaces, kernel and image. Linear independence, spans, bases and dimension Matrix of a linear map, change of basis, linear operators, similar matrices. Rank, nullity and the Rank-Nullity theorem Inner product spaces: orthogonality, Cauchy-Schwarz inequality and applications. Gram-Schmidt process: orthonormal bases, orthogonal matrices and QR decomposition, orthogonal subspaces. Determinants and adjugates: properties and computation; invertibility of matrices. Eigenvalues, eigenvectors and eigenspaces; characteristic polynomial, algebraic and geometric multiplicities, diagonalisability. Self-adjoint operators, symmetric/Hermitian matrices and their orthogonal diagonalisation. Connections: Mathematical research at the University of Bath, including applications of degree-level mathematics in industry and society, outreach, and advocacy.

Course availability:

MA12004 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.