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Introduction to Algebra and Modern Mathematics

 

Introduction to Algebra and Modern Mathematics

An in-depth study of the mathematical arts and sciences traditionally known as the quadrivium (“four ways”): geometry, arithmetic, astronomy, and music. You will read classic works in each of the four arts and sciences and begin to discover the essential role that these mathematical studies have in a liberal education.

LOCATION: Online

Wednesdays & Thursdays 16:30 - 18:00

Cost: €1.995. There are grants available.

Language: English

DATE: 14 February - 8 May 2024

DEADLINE: 22 January 2024


In this course on the quadrivium, you will learn about ancient and modern accounts of geometry and arithmetic as distinct arts and sciences. You will see how alternative ways of understanding geometry and arithmetic may open new possibilities for discovery—especially in the development of algebra and number theory. You will elaborately examine the works of François Viète, René Descartes, Leonardo of Pisa (“Fibonacci”), Blaise Pascal, Gottfried Wilhelm Leibniz, Leonhard Euler, Richard Dedekind, and Georg Cantor, among others.

This course is open for anyone interested in learning more about mathematics as a liberal art. The instructors, dr. Jeff Lehman and dr. Andrew Seeley, are excellent professors who will help you to get a deeper and richer understanding of the foundations of mathematics.

This course will take place twice a week – online.

Note: Good candidates can apply for a grant to follow this course. Read more about our grants and scholarships here.

François Viète, Introduction to the Analytic Art; Standard Enumeration of Geometric Results
René Descartes, Discourse on Method; Geometry; Rules for the Direction of the Mind
Leonardo of Pisa (“Fibonacci”), Liber Abacci (The Book of Calculation)
Blaise Pascal, Mathematical Works
Sean Collins, “On the Use of Symbols
Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (sel.)
Gottfried Wilhelm Leibniz, Paper on Differential Calculus
Leonhard Euler, On the Completion of Algebra (Elements of Algebra)
Richard Dedekind, Essay on the Theory of Numbers
Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers

The students will only need to purchase the works below. You can find the edition we will be using by following the inserted links. All other entire works and selections will be provided as PDFs.

René Descartes, Discourse on Method; Geometry; Rules for the Direction of the Mind
Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (sel.)
Richard Dedekind, Essay on the Theory of Numbers

For whom is this course?

Advanced students at master's level. People who already graduated are also welcome.


Who teach this course?

Dr. Jeffrey Lehman & dr. Andrew Seeley


What's the cost?

This intensive course costs €1995 per semester. A number of scholarships are available for good candidates. Candidates can apply for a grant by sending a motivation that shows that they have a high academic level and that also briefly explains why he or she needs the grant to be able to pay their own contribution. Various grants are available for 50, 75 and 100 percent of the total cost.


When is this course being taught?

Wednesday & Thursday 16:30-18:00. The semester runs 12 weeks between 14 February and 8 May 2024.


What do I receive after the course?
You will receive a certificate. To successfully complete this course, good preparation and active participation are necessary; the student must also attend every lecture.

How do I apply?

The deadline is January 20, 2024, 17:00. You will be told before January 27, 2024 whether you have been accepted. You will be told before February 1, 2024 whether you will receive a grant, if you have applied for one.


Reading outlines

For most of the reading assignments, students are to prepare outlines (or detailed reading notes) based upon the readings. Such outlines will help students stay current on the material and also will promote better understanding of the readings and participation in the class discussions. The structure of the outline is up to the student, but all outlines must be clear, orderly, and comprehensive for each reading for which an outline is assigned. In order to receive credit, each outline must be completed prior to the class session for which the reading was assigned. All outlines will be submitted for grading at the time of the final exam.


Classroom discussions

All class sessions will be conducted as “seminars,” or Socratic conversations. Students are expected to actively participate in the discussion for the duration of each class session.


Final Exam

Students will complete a cumulative final exam at the end of the course.