Course Exam—MATH 409

MATH 409 (Number Theory) is a course in elementary number theory, the branch of mathematics concerned with the properties of numbers, including such things as divisibility, prime numbers, modular arithmetic, quadratic congruences, Pythagorean triples, the theorems, conjectures, definitions and lemmas that permit exploration of these topics, and more.  This course is a three-credit upper level mathematics course that has five prerequisites, which include MATH 265 (Introduction to Calculus I), MATH 266 (Introduction to Calculus II), MATH 270 (Linear Algebra I), MATH 271 (Linear Algebra II), and MATH 309 (Discrete Mathematics).  Students may use equivalent math courses from other universities towards the prerequisite.

If you are interested in learning more about Introduction to Calculus I or Discrete Mathematics, read my MATH 265 and MATH 309 Course Exam articles!

Number Theory is made up of ten core units, and is graded on a course notebook component at seventy percent, a midterm examination weighing ten percent, and a final examination weighing twenty percent.  To receive credit for this course, students much achieve a course composite grade of at least sixty percent and the student must achieve a combined grade of at least fifty percent on the midterm and final examinations.  This means that students do not need to achieve fifty percent on each of the exams.  The ten units within this course cover complex mathematical concepts such as modularity, prime numbers, quadratic reciprocity, primitive roots, cryptography (writing or solving codes), rational approximation, and linear Diophantine equations.

Dr.  James Greenwood-Lee was born and raised in Calgary, Alberta and is the course coordinator for MATH 409 (Number Theory), as well as SCIE 326 (Scientific Reasoning), MATH 244 (Business Mathematics), MATH 481 (Mathematical Modeling II), MATH 495 (Mathematics Projects), and MATH 496 (Mathematics Projects).  He joined Athabasca University in 2010 as a tutor and became an Assistant Professor in 2015.  He completed an undergraduate degree in Zoology at the University of Calgary and then went to Queen’s for his graduate studies in Mathematics.  After that he moved back to Calgary because he and his wife wanted their children to grow up close to their family.  He states, “Now I have two awesome kids, who are continually besting me at everything!”

If you are interested in learning more about Scientific Reasoning and Business Mathematics, read my SCIE 326 and MATH 244 Course Exam articles!

Dr.  Greenwood-Lee states, “Math 409 – Number Theory – is an upper graduate mathematics course geared towards our applied mathematics majors.  It is a course in elementary number theory, the branch of mathematics concerned with the properties of numbers.”

He continues, “This is a neat course in which students are guided on a voyage of discovery.  While the course presents key theorems from number theory, proofs are not presented.  Rather students must develop their own proofs! The course content is a carefully arranged series of problems, exercises, and theorems, which students are expected to work through on their own, and present in their course notebooks.  The sequence of exercises and theorems is arranged so that it leads the student through the course, but certain gaps are left, where students must be able to make a creative contribution.”

He adds, “The evaluation of this course is heavily focused on the work students do on this journey.  Specifically, students are evaluated on their course workbooks.  For each unit, students are asked to showcase six Theorem proofs or exercises that represent their best work.  A midterm and final exam are also used to evaluate students.  The midterm focuses on the first half of the course and final focuses on the last half of the course.”

Dr.  Greenwood-Lee states, “Obviously, a course like Math 409, not only requires hard work, but also a high level of interest.  This is not a course to try to slog through.  To be successful I strongly encourage students to engage with myself as they work the material, as well as with other students.”

He concludes, “Who should take Math 409? This is a great course that I would recommend to anyone with a genuine interest in learning more about mathematics and how mathematics is conducted.  Students will not only take away foundational knowledge of number theory but will also develop the necessary tools to develop and present formal mathematical proofs.”

Whether this course is a degree requirement of yours or you are interested in the topics discussed above, MATH 409 will have you learning interesting mathematical proofs and will challenge your skills in mathematics.  If you have any questions or concerns regarding MATH 409 or any of the courses that he coordinates, or you would like to provide feedback on any of the courses, Dr.  James Greenwood-Lee encourages you to contact him at

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