Historical Development of Mathematics

Syllabus

Class Calendar

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  • 3/9/2026: We finished the Number Systems Presentation, and then talked about different types of numbers. We discussed how we could show 1 and \(\sqrt{2}\) are incommensurable. Then we started looking at constructible numbers; here is an updated copy of the constructible numbers sheet.
  • 3/4/2026: We discussed Sketches 1-3 and then spent time discussing number systems. We ended looking at the Dresden Codex. We will pick up there on Monday after discussing the next set of Sketches.
  • 3/2/2026: History in a Nutshell Exam
  • 2/23/2026: picture of a snowing cloud Snow Day picture of a snowing cloud We are still on track to finishe the Unit 1 material Wednesday so we will still have the Unit 1 Exam next Monday, 3/2/2026.
  • 2/18/2026: We discussed the material in the reading and video and then started looking at the mathematics behind the work of Galois and Abel. To do this we worked through the first three sections of the Great Big Galois Example Slides. We saw, using DeMoivre’s Theorem, that all the roots of \(x^n-1\) are equal to a power of \[\omega=\cos\left(\frac{2\pi}{n}\right)+i\sin\left(\frac{2\pi}{n}\right),\] and that all the roots of \(x^n+1\) are powers of \[\zeta=\cos\left(\frac{\pi}{n}\right)+i\sin\left(\frac{\pi}{n}\right).\] We also noted that the roots always form a regular \(n\)-gon if we connect them. We will discuss these ideas further in the next class.
  • 2/11/2026: We discussed the Indian Algorithm for finding square roots.
  • 2/9/2026: We discussed the reading for the first half of class, then reviewed the Mesopotamian way of approximating roots. We then looked at how the Chinese approximated roots.
  • 2/4/2026: We discussed the video The Story of Maths: The Language of the Universe. Then we looked at a Mesopotamian approach to finding square roots and an application of that to finding a diagonal of a rectangle. For next time complete the assigned reading; we will look at Chinese and Indian algorithms for finding square roots both based on a base 10 number system.
  • 2/2/2026: Today we discussed the readings on Indian and Arabic Mathematics. As you are doing the readings and watching the video be sure to pay close attention to the history and cultures as well as the math. We then reviewed material on Egyptian arithmetic and went over the first problem from the Moscow Papyrus. You should complete the second Moscow Papyrus problem on your own and be sure to watch the next video prior to the next class.
  • 1/28/2026: Today we worked through most of sections 1 through 3 of the the Rosetta Stone Packet (https://tinyurl.com/3vppjdem). Finish up and review those sections so that we can work on sections 4 and 5 in class. Also be sure to do the reading listed on the syllabus.
  • 1/26/2026: picture of a snowing cloud Snow Day picture of a snowing cloud: Please be sure that you have finished the first reading and have watched The Story of Maths: The Language of the Universe by Wednesday. Since we finished The Story of 1 last Wednesday we will be able to stick to our schedule as listed on the syllabus.
  • 1/21/2026: We went over the Syllabus and Watched The Story of 1.

Unit 1: Overview of The History of Mathematics

Unit 2: Evolution of Numbers

  • Text Sections: Sketches 1-5 (pp. 67-102), Sketch 17 (pp.179-186), Sketch 29 (pp. 271-278)
  • Assignment Due 4/6/2026: Sketch 3 – 4 (p.85); Sketch 4 – 4 (p.93); Sketch 5 – 2 (p.101); Sketch 17 – 3 & 4 (p.185); Sketch 29 – 2 (p.277)
  • Exam on 3/30/2026

Unit 3: Algebra and Calculus

  • Text Sections: Sketches 8 – 11 (pp. 115-140), 30 (pp. 279-286)
  • Assignment Due 4/27/2026: Sketch 9 – 2 & 6 (p.127); Sketch 11 – 4 (p.139); Sketch 30 – 2 & 3 (p.285)
  • Exam on 4/20/2026

Unit 4: Geometry Through the Ages

  • Text Sections: Sketches 7 (pp.109-114), 12 (pp.141-148), 14-16 (pp.157-178), 19 & 20 (pp. 195-202)
  • Assignment Due 5/15/2026 by 3pm: Sketch 7 – 2 (p.113); Sketch 12 – 3 (p.147); Sketch 14 – 3 (p.163); Sketch 16 – 2 (p.177); Sketch 19 – 3 (p.201); Sketch 20 – 5 (p.205)
  • Exam on 5/11/2024

Primary Source Project

Select an activity from the TRIUMPHS (TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources) Project which you can learn about here: https://triumphs.ursinus.edu/. For your Primary Source Project you will need to complete one of these projects, then research the history of a typical secondary education mathematics topic and use that research to create a similar project for that topic.

Overview

Details

Dates

Sources

Links and Handouts