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MATH1561: SINGLE MATHEMATICS A

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 1
Credits 20
Availability Available in 2024/2025
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • A level Mathematics at Grade A or better, orequivalent.

Corequisites

  • None.

Excluded Combinations of Modules

  • Calculus I (Maths Hons) (MATH1081), Calculus (MATH1061), Linear Algebra I (Maths Hons) (MATH1091), Linear Algebra I (MATH1071), Mathematics for Engineers and Scientists (MATH1551)may not be taken with or after thismodule.

Aims

  • This module has been designed to supply mathematics relevant tostudents of the physical sciences.

Content

  • Basic functions and elementary calculus: includingstandard functions and their inverses, the Binomial Theorem, basicmethods for differentiation and integration.
  • Complex numbers: including addition, subtraction,multiplication, division, complex conjugate, modulus, argument, Arganddiagram, de Moivre's theorem, circular and hyperbolicfunctions.
  • Single variable calculus: including discussion of realnumbers, rationals and irrationals, limits, continuity,differentiability, mean value theorem, L'Hopital's rule, summation of series,convergence, Taylor's theorem.
  • Matrices and determinants: including determinants, rulesfor manipulation, transpose, adjoint and inverse matrices,Gaussian elimination, eigenvalues and eigenvectors,
  • Groups, axioms, non-abelian groups

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will: be able to solve arange of predictable or less predictable problems inMathematics.
  • have an awareness of the basic concepts of theoreticalmathematics in these areas.
  • have a broad knowledge and basic understanding of thesesubjects demonstrated through one or more of the following topicareas: Elementary algebra.
  • Calculus.
  • Complex numbers.
  • Taylor's Theorem.
  • Linear equations and matrices.
  • Groups

Subject-specific Skills:

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
  • Initial diagnostic testing fills in gaps related to the wide variety of syllabuses available at Mathematics A-level.
  • Tutorials provide the practice and support in applying the methods to relevant situations as well as active engagement and feedback to the learning process.
  • Weekly coursework provides an opportunity for students to consolidate the learning of material as the module progresses (there are no higher level modules in the department of Mathematical Sciences which build on this module). It serves as a guide in the correct development of students' knowledge and skills, as well as an aid in developing their awareness of standards required.
  • The end-of-year written examination provides a substantial complementary assessment of the achievement of the student.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures633 per week for 21 weeks1 Hour63 
Tutorials9Weeks 3, 5, 7, 9 (Term 1) and 13, 15, 17, 19 (Term 2), plus 1 revision tutorial in Easter term. 1 Hour9Yes
Support classes18Weekly in weeks 2-10 and 12-20.1 Hour18 
Preparation and Reading110 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 90%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 hours100Yes
Component: Continuous AssessmentComponent Weighting: 10%
ElementLength / DurationElement WeightingResit Opportunity
Fortnightly assessments during the first 2 terms. Normally, each will consist of solving problems. Students will have about one week to complete each assignment.100Yes

Formative Assessment

40 minute collection paper in the beginning of Epiphany term. Fortnightly formative assessment.

More information

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