NS2022: Mathematics for Science II

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Credits: 10

Length: Continuous throughout the year

 

Module Synopsis: 

Mathematics is the language of much of science and is an integral part of the Natural Science programme. This module is designed to support your core work. Since you will each be entering the course with very different backgrounds in mathematics the course is designed flexibly to provide a gentle introduction to those who need it without taking up the time of those who have already had a broad experience in mathematics. To achieve this we ask students who have already come across the material to submit work ahead of classes. If this shows a mastery of the material then no further action is required. Otherwise you will join students who have not previously come across the material in two classes, after which you can have two attempts at completing the work for a Unit. In this way we expect each student to achieve mastery of all the material.

Each mathematics unit is broken down in to two sections: competency based (section A) and Application (section B) questions. The Competency-based section covers the material required to test that you have attained an adequate level of mastery of all the techniques of that Unit.

The Applications questions develop this mastery, providing additional practice in the techniques with particular focus on applying the mathematics to quantitative scientific problem solving, many examples of which you will address in your Core modules.

Topics:

  • Complex Numbers: basic algebraic calculations with complex numbers; geometrical representation of complex numbers; represent sine and cosine in terms of exp(I θ); De Moivre’s theorem
  • Matrices: algebraic manipulations of matrices; determinant and inverse matrices; linear systems of equations; eigenvalues and eigenvectors
  • Probability: defining probabilities; variable categories; probability distributions (e.g. binomial, Poisson, normal); median and modes of sets; permutations and combinations
  • Statistics: statistical variables; constructing frequency distributions; central tendency and dispersion of datasets; normal and non-normal frequency distributions; plotting statistical representations; correlation analysis; linear regression
  • Vectors: algebraic manipulation of vectors; parallelogram law; geometrical interpretation; scalar, vector and triple products; manipulating vector identities

 

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