Thomas Chaplin

Mathematics

Linear Algebra

• Down with Determiannts! by Sheldon Axler – An al­ter­na­tive ap­proach to fun­da­men­tal con­cepts in lin­ear al­ge­bra such as eigen­val­ues and the char­ac­ter­is­tic poly­no­mi­als, with no ref­er­ence to de­ter­mi­nants.
• Essence of Linear Algebra by 3Blue1Brown – A vi­sual in­tro­duc­tion to vec­tor spaces, lin­ear maps, ma­trix mul­ti­pli­ca­tion, de­ter­mi­nants and a vi­sual jus­ti­fi­ca­tion for Cramer’s rule.

Topology

• From an oc­ta­gon to a genus 2 sur­face by Jos Leys

Complex Analysis

• Visualizing Complex Roots of Quadratic Equations by Aran Glancy
• Conformal by David Bau – A use­ful tool for vi­su­al­is­ing func­tions on the com­plex plane. You can also use pa­ra­me­ters to an­i­mate through fam­i­lies of com­plex func­tions or even ap­ply your favourite com­plex func­tion to the world map.

Maths com­mu­ni­ca­tion

• Manim – Self-described as ‘a com­mu­nity-main­tained Python li­brary for cre­at­ing math­e­mat­i­cal an­i­ma­tions’. Orig­i­nally de­vel­oped by the maths YouTuber 3Blue1Brown, this pack­age makes cre­at­ing beau­ti­ful, ed­u­ca­tional videos a breeze.

Software Development

• DuckDNS – A DyanmicDNS ser­vice set up by soft­ware de­vel­op­ers. Com­pletely free, with­out ads or the need to pe­ri­od­i­cally re­new ac­count. Su­per easy to setup on a wide va­ri­ety of op­er­at­ing sys­tems or routers.
• re-frame – A frame­work for writ­ing ClojureScript web apps. Lever­age the speed, power and com­mu­nity of React, in a data-ori­ented, func­tional frame­work. Iso­late side ef­fects and co-ef­fects; write your view as a pure func­tion of your state.