**MATH UN2015 – Linear Algebra & Probability**

MATH UN2015 features linear algebra with a focus on probability and statistics. The course covers the standard linear algebra topics: systems of linear equations, matrices, determinants, vector spaces, bases, dimension, eigenvalues and eigenvectors. It also teaches applications of linear algebra to probability, statistics and dynamical systems giving a background sufficient for higher level courses in probability and statistics. The topics covered in the probability theory part include conditional probability, discrete and continuous random variables, probability distributions and the limit theorems, as well as Markov chains, curve fitting, regression, and pattern analysis. The course contains applications to life sciences, chemistry, and environmental life sciences. No a priori background in the life sciences is assumed.

MATH UN2015 – Linear Algebra & Probability is a course best suited for students who wish to focus on applications and practical approach to problem solving, rather than abstract mathematics and mathematical proofs. It is recommended to students majoring in engineering, technology, life sciences, social sciences, and economics.

Students majoring in mathematics should takeMATH UN2010 – Linear Algebra, which focuses on linear algebra concepts, and provides an introduction to writing mathematical proofs.

**Prerequisites**

MATH UN1101 – Calculus I (or equivalent) is strongly recommended.

**Textbooks**:

- Otto Bretscher,
*Linear Algebra with Applications,***5th edition**(Publisher link) - Cliff Taubes,
*Lecture notes on Probability, Statistics and Linear Algebra*

**Topics**

The sequence of topics covered is as follows.

- Linear Algebra
- Linear equations
- Linear transformations
- Subspaces of R^n and their dimensions
- Orthogonality and lest squares
- Determinants
- Eigenvalues and eigenvectors
- Symmetric matrices

- Probability
- Basic notions from probability theory
- Conditional probability
- Random variables
- Probability distributions
- Central limit theorem
- Markov processes

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