Classical Algebra

This high school algebra course takes a unique approach by: Exploring the historical roots of algebra, showing how concepts are connected-
Focusing on understanding underlying ideas rather than just memorizing formulas-
Challenging students to see math as more than just problem-solving: it's connected to other subjects like philosophy and literature-

By taking a deeper look at algebra, students will gain a richer understanding of the subject and its place in the world.

The course is organized around the classic textbook The Elements of Algebra, by Leonhard Euler, one of the greatest mathematicians of the 18th century. Additional readings from Diophantus, Viete, and Cardano will be provided for historical context as we undertake the systematic study of algebra.

Class time will be spent discussing key concepts and working out problems. Students will be expected present weekly, guiding the class through a selected problem or proof. Students should expect to spend an average of 1 – 1.5 hours per school day studying & working problems. During the week, students will be responsible for keeping up with weekly assignments & practice problems. Apart from the exams, students are expected to correct their own homework & assignments. To evaluate and encourage broad-scale analysis, three essays will also be assigned.

Prerequisites

Students should have completed PreAlgebra, be self-motivated, and be strong readers. Please note that students who struggled in PreAlgebra may have a difficult time in this course, as we maintain a fairly brisk pace.

Course Objectives

To gain a more profound understanding & mastery of algebra than is possible via traditional textbooks. To learn to see mathematics as a discipline of beauty, to comprehend the interrelationship of algebraic theorems and solution methods To learn to think in precise and creative terms in mathematics and beyond.

Texts

The Elements of Algebra by Leonhard Euler Additional texts will be provided in PDF form

FAQ

Q: Is this Algebra 1 or Algebra 2?A: This course is something of an accelerated Algebra 1 course. Like Algebra 1, it is primarily concerned with the solution of first degree polynomials, and unconcerned with trigonometry or graphing. Unlike Algebra 1, however, it covers several topics not introduced until later, such as logarithms and solutions to second and third degree polynomials. If we had to put a label on it, the course is something like Algebra 1 & 1/2.
Q: My student has already taken Algebra 1. What would he get out of this course? Would he just be repeating a year of math?

A: While there will be quite a bit of overlap, one of they differences is that we will be working a good bit with primary sources. In other words, compared to the typical approach to algebra, one has a completely different experience learning to solve problems by observing how Diophantus or Viete approached them. In the first case, one primarily learns methods. In the second, one learns to follow a master--not only by observing the master's methods, but by observing the very questions that drove those methods.
Q: If my student takes this course, what should he take next year?A: This course meets the requirements of Algebra 1, so he should be ready to advance to Geometry or Algebra 2, depending on the curriculum sequence you're using.
Q: Should my student take Classical Algebra first, or Euclidean Geometry first?A: The ideal sequence is Euclidean Geometry first, followed by Classical Algebra. While Euclidean Geometry is not a prerequisite for this course, it provides a valuable foundation and context in which to understand these later mathematical developments. One can properly appreciate Algebra only after a careful study of Geometry.