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Linear Algebra & Probability

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.

Math majors, joint majors, and math concentrators should take MATH UN2010 – Linear Algebra, which focuses on linear algebra concepts and foundations that are needed for upper-level math courses. UN2015 (Linear Algebra and Probability) does NOT replace UN2010 (Linear Algebra) as prerequisite requirements of math courses. Students will not receive full credit for both courses UN2010 and UN2015. 


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
    1. Linear equations
    2. Linear transformations
    3. Subspaces of R^n and their dimensions
    4. Orthogonality and lest squares
    5. Determinants
    6. Eigenvalues and eigenvectors
    7. Symmetric matrices
  • Probability
    1. Basic notions from probability theory
    2. Conditional probability
    3. Random variables
    4. Probability distributions
    5. Central limit theorem
    6. Markov processes

 

 

 

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