Per Alexandersson

Course material

Here is a collection of supplementary exercises, most of them with complete solutions for various courses I have taught. I have taught a lot of linear algebra and discrete mathematics, so I have plenty of resources to share. Most problems have complete solutions, and most solutions have been used in several courses. If you find any errors, please let me know. Also, if you find the material helpful, please send me an email, I am happy to get any type of feedback!

Linjär algebra (Svenska)

(pdf) Linjär algebra I — En samling med problem och lösningar för första terminen i matematik.

(pdf) Linjär algebra II — En samling med problem och lösningar i nästa kurs. Generella vektorrum, SVD-uppdelning, determinanter med mera. Mobilvänlig version.

(pdf) Linjär algebra för lärare — En samling med problem, lösningar samt sammanfattning av linjär alebra för lärarlyftet.

Discrete mathematics (English)

(pdf) Discrete mathematics — A collection of exercises and solutions in discrete mathematics. Examples from counting (binomial coefficients, pigeon-hole principle, inclusion-exclusion), and problems regarding groups, rings and fields, as well as Burnside's lemma. Suitable for KTH courses SF1671, SF1630 as well as the Stockholm University course MM5013, Algebra och kombinatorik.

(pdf) Random graphs. — Random graphs and the probabilistic method. For master students.

(pdf) Proofs by induction. — A collection of proofs by induction with some solutions. Perfect for the first semester math studies.

Calculus (English)

(pdf) Multivariate Calculus. — A collection of problems and some solutions in multivariate Calculus. This is based on Calc 114, that I taught at University of Pennsylvania.

(pdf) Min-max problems.

(pdf) Midterm 1a, Calc 114 with solutions.

(pdf) Midterm 2a, Calc 114 with solutions.

(pdf) Midterm 2a extra, Calc 114 with solutions.

(pdf) Midterm 3a, Calc 114 with solutions.

(pdf) Midterm 3 extra, Calc 114 with solutions.

(pdf) Midterm 4 takehome, Calc 114 with solutions.

Other documents

Common mistakes when writing mathematics (English)

Common mistakes — A list of common mistakes when typing up mathematics.

Klassiska fraktaler (Svenska)

(pdf) Klassiska fraktaler — En introduktion till algoritmerna bakom några av de mest kända fraktalerna.