__MATH 366 __(Complex Variables I) is a three-credit, upper-level mathematics course that is an introductory complex variable course covering complex numbers, complex variable functions, continuity, limits, derivatives, transcendental functions, integration on the complex plane, infinite series with complex variables, and the residue theorem with some of its applications. MATH 366 requires students to take MATH 365 (Multivariable Calculus) or an equivalent course from another institution as a prerequisite and it has a challenge for credit option if interested.

Complex Variables I is made up of six units, four assignments weighing ten percent each, one midterm examination worth thirty percent, and a final examination that weighs thirty percent. To receive credit for MATH 366, students must submit all the course assignments and complete them to the satisfaction of the assigned tutor. Students must also achieve a grade of at least a “D” or fifty percent on each examination, and a course composite grade of at least a “D” or fifty percent.

Craig Belair, twenty-nine years old and from Calgary, enrolled at Athabasca University in September of 2017. He is currently enrolled in the Bachelor of Science in Applied Math program at Athabasca University and has taken MATH 366. He provides a brief introduction, stating “I was working retail jobs through my early 20’s and didn’t feel particularly inspired by my work, so I decided to enroll in Athabasca University. I had enjoyed Math, particularly calculus in high school, so I decided to go for a BSc in Mathematics. I am currently working part-time as a math tutor for grades two to twelve. I appreciate the challenge of trying to explain a concept in many ways, trying to see what explanation best connects with the student. In my spare time I like to go for hikes, workout at the gym, go drinking with friends, watch Netflix, and play chess/various online games.”

Craig explains MATH 366, stating “MATH 366 is a senior-level math course that delves into the complex numbers and explores applying concepts from elementary calculus on functions of complex variables. The course starts out by covering some of the basic properties of complex numbers and then moves onto interpreting a lot of the fundamental ideas from real variable calculus in the complex number system. For example: what does it mean for a complex function to have a derivative? How do we integrate complex functions? What special properties do analytic complex functions have? The course concludes by going over series representation of complex functions, and ways we can use the complex integration to solve real valued calculus problems.”

As for the structure of the course, he explains that it is pretty simple, stating “The course is broken up into six units. There are four assignments, two of which each cover two units of the course, and the other two which each cover one unit of the course. The assignments are each worth ten percent of your final grade. The assignments are a mix of computational questions, and some more interesting proofing questions or questions that test a students’ understanding. There is a midterm exam that covers units one through three and a cumulative final exam. Each of the exams are worth thirty percent. As is the case with most math exams, the exams are about ten written response questions. The exams covered mostly the computational aspects of the course, which made them a fair bit easier than the assignments. Reading the textbook is one hundred percent necessary to complete this course.”

Craig states that he would definitely recommend this course to other students, as “This was one of the math courses I enjoyed most from Athabasca, a close second would have to be MATH 409. Needless to say, I would only recommend it to students who had already taken Calculus I/II and Multivariable Calculus, as the course builds heavily on topics covered in those courses. I think if a student has a good foundation in Calculus, this course is not very difficult.”

As for any tips or tricks, he believes that “The most important thing in this course is to be confident with the prerequisite material. If you do not feel confident with Taylor series expansions from Calculus II, review them before taking this course. Similarly, if you don’t feel confident with parametric representations of curves, or partial derivatives, review that material. If those foundational skills are there, I think the course will be a breeze.”

When asked how communications with his tutor was, he explains “My tutor (Ming Kou) has been super helpful. He is always very quick to respond, to mark my assignments, and willing to answer any questions I have had. His assignment feedback is informative, and if I have any questions regarding it, he is always willing to answer them.”

Whether MATH 366 is a degree or program requirement of yours, or the topics that were discussed above are of interest to you, Complex Variables I will have you learning some interesting and complex mathematical concepts.