I give approx 24 first-year lectures in Michaelmas Term. The first few lectures are on complex numbers. The main event, however, is linear algebra (vectors & matrices), which will start on Friday of week 1.

## Complex numbers

Topics: basic arithmetic operations; the Argand diagram; modulus and argument (phase) and their geometric interpretation; curves in the Argand diagram. De Moivre’s theorem. Elementary functions (polynomial, trigonometric, exponential, hyperbolic, logarithmic) of a complex variable.

## Vectors and matrices (aka linear algebra)

This provides an introduction to linear algebra, giving you a more grown-up appreciation of vectors and matrices than you may already have encountered in school. Here is an overview of the lectures, week by week.

There are many good textbooks on this topic (as well as even more uninspiring ones), all of which should be easy to find in libraries.

• I strongly recommend Andre Lukas’s notes and problems for this course from MT2017. My lectures will cover the same topics in roughly the same order. I’m recycling his problem sets (below) from last year.

• Linear algebra by Lang

• Mathematical methods for physics and engineering by Riley, Hobson & Bence is good for exercises and concrete examples.

### Problems

• Problems 1 on vector spaces and 3d geometry (covered by Monday of week 3)
• Problems 2 on matrices, linear equations and maps (by end of week 4)
• Problems 3 on determinants and scalar products (end of week 5)
• Problems 4 on eigenvalues and eigenvectors (end of course, Monday week 7)