MS221 Exploring Mathematics http://www.gandraxa.com/ms221_exploring_mathematics.xml img/ms221_menu.jpg Block D study books of course MS221 home.xml Home learning.xml Learning MS221 Exploring Mathematics mst121_using_mathematics.xml MST121 Using Mathematics c46_certificate_in_mathematics.xml C46 Certificate in Mathematics hg gandraxa.com Herbert Glarner 2008Mar24 Original HTML version 2011Feb02 Recoded in XLM http://en.wikipedia.org/wiki/Open_University Open University on Wikipedia http://www3.open.ac.uk/courses/bin/p12.dll?C01eMS221 Description of MS221 on OU site (without syllabus) Syllabus Handbook Block A: Mathematical Exploration Block B: Exploring Iteration Block C: Calculus Block D: Structure in Mathematics Computer Books

Abstract This page provides an overview of the Open University course's syllabus.

Note The content given is valid for the presentation which started in February 2008. Later presentations may differ in more than one aspect.

 Syllabus Handbook img/ms221_hb.jpg Handbook ISBN 0 7492 6647 3
88 pages
  • The Greek alphabet
  • SI units
  • Mathematical modelling
  • Some useful graphs
  • Notation
  • Glossary
  • Background material for MST121 and MS221
  • Definitions and results in MST121 and MS221
    •      Block A: Mathematical Exploration
    Chapter A1: Exploring sequences img/ms221_a1.jpg A1: Exploring sequences ISBN 0 7492 9324 1
    47 pages
  • The golden ratio
  • Fibonacci numbers and their properties
  • Linear second-order recurrence sequences
  • Exploring linear second-order recurrence sequences with the computer
  • Proving identities
    •
    Chapter A2: Conics img/ms221_a2.jpg A2: Conics ISBN 0 7492 9329 2
    60 pages
  • What is a conic?
  • Conics in standard position
  • The focus-directrix property
  • Quadratic curves
  • Parametrising conics
  • Conics on the computer
    •
    Chapter A3: Functions from geometry img/ms221_a3.jpg A3: Functions from geometry ISBN 0 7492 9334 9
    60 pages
  • Functions
  • Isometries
  • Trigonometric formulas
  • Quadratic curves revisited
  • Isometries on the computer
    •
    Block B: Exploring Iteration
    Chapter B1: Iteration img/ms221_b1.jpg B1: Iteration ISBN 0 7492 3998 1
    60 pages
  • Iterating real functions
  • Classifying fixed points
  • Composition of functions
  • Iterating real functions with the computer
  • The Binomial Theorem
    •
    Chapter B2: Matrix transformations img/ms221_b2.jpg B2: Matrix transformations ISBN 0 7492 4032 6
    68 pages
  • Vectors and matrices
  • Linear transformations
  • Composite and inverse transformations
  • Affine transformations
  • Visualising affine transformations
    •
    Chapter B3: Iteration with matrices img/ms221_b3.jpg B3: Iteration with matrices ISBN 0 7492 4035 1
    63 pages
  • Fixed points and invariant lines
  • Eigenvalues and eigenlines
  • Using eigenvalues and eigenlines
  • Iterating linear transformations
  • Iterating linear transformations with the computer
    •
    Block C: Calculus
    Chapter C1: Differentiation img/ms221_c1.jpg C1: Differentiation ISBN 0 7492 2293 2
    63 pages
  • Differentiation
  • Differentiating combinations of functions
  • Graph sketching
  • Newton-Raphson method
  • Differentiation with the computer
    •
    Chapter C2: Integration img/ms221_c2.jpg C2: Integration ISBN 0 7492 5560 9
    64 pages
  • Integration
  • Integration by parts
  • Integration by substitution
  • Volumes of solids of revolution
  • Integration with the computer
    •
    Chapter C3: Taylor polynomials img/ms221_c3.jpg C3: Taylor polynomials ISBN 0 7492 5561 7
    60 pages
  • Linear and quadratic Taylor polynomials
  • Taylor polynomials
  • Taylor series
  • Manipulating Taylor series
  • Taylor series with the computer
    •
    Block D: Structure in mathematics
    Chapter D1: Complex numbers img/ms221_d1.jpg D1: Complex numbers ISBN 0 7492 6652 X
    55 pages
  • The origins of complex numbers
  • Complex numbers
  • The geometry of complex numbers
  • Roots of polynomials
  • Complex exponentials
  • Complex numbers and Mathcad
    •
    Chapter D2: Number theory img/ms221_d2.jpg D2: Number theory ISBN 0 7492 6653 8
    48 pages
  • Congruence
  • Divisibility tests
  • Modular arithmetic
  • Cryptography
  • Number theory and Mathcad
    •
    Chapter D3: Groups img/ms221_d3.jpg D3: Groups ISBN 0 7492 6654 6
    60 pages
  • Symmetry
  • Groups
  • Isomorphic groups
  • Groups in action
    •
    Chapter D4: Proof and reasoning img/ms221_d4.jpg D4: Proof and reasoning ISBN 0 7492 2296 3
    48 pages
  • Aspects of proof
  • Implication and deduction
  • Proof by mathematical induction
    •
    Computer Books
    Block A: Mathematical Exploration img/ms221_acb.jpg Block A: Mathematical Exploration ISBN 0 7492 6651 1
    35 pages
  • Exploring linear second-order recurrence sequences with the computer
  • Conics on the computer
  • Isometries on the computer
    •
    Block B: Exploring Iteration img/ms221_bcb.jpg Block B: Exploring Iteration ISBN 0 7492 6648 1
    36 pages
  • Iterating real functions with the computer
  • Visualising affine transformations
  • Iterating linear transformations with the computer
    •
    Block C: Calculus img/ms221_ccb.jpg Block C: Calculus ISBN 0 7492 6649 X
    30 pages
  • Differentiation with the computer
  • Integration with the computer
  • Taylor series with the computer
    •
    Block D: Structure in Mathematics img/ms221_dcb.jpg Block D: Structure in Mathematics ISBN 0 7492 6650 3
    28 pages
  • Complex numbers and Mathcad
  • Number theory and Mathcad
  • Symmetry
    •