An introduction to geometry with a selection of topics from the following: symmetry and symmetry groups, finite geometries and applications, non-Euclidean geometry.

This course is an introduction to axiomatic set theory and its methods. Set theory is a foundation for practically every other area of mathematics and is a deep, rich subject in its own right. The course will begin with the Zermelo-Fraenkel axioms and general set constructions. Then the natural numbers and their arithmetic are developed axiomatically. The central concepts of cardinality, cardinal numbers, and the Cantor-Bernstein theorem are studied, as are ordinal numbers and transfinite induction. The Axiom of Choice and its equivalents are presented along with applications.

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.

The main problems of coding theory and cryptography are defined. Classic linear and non-linear codes. Error correcting and decoding properties. Cryptanalysis of classical ciphers from substitution to DES and various public key systems [e.g. RSA] and discrete logarithm based systems. Needed mathematical results from number theory, finite fields, and complexity theory are stated.

An intuitive and conceptual introduction to general relativity with emphasis on a rigorous treatment of relevant topics in geometric analysis. The course aims at presenting rigorous theorems giving insights into fundamental natural phenomena. Contents: Riemannian and Lorentzian geometry (parallelism, geodesics, curvature tensors, minimal surfaces), Hyperbolic differential equations (domain of dependence, global hyperbolicity). Relativity (causality, light cones, inertial observes, trapped surfaces, Penrose incompleteness theorem, black holes, gravitational waves).

Applications of complex analysis to geometry, physics and number theory. Fractional linear transformations and the Lorentz group. Solution to the Dirichlet problem by conformal mapping and the Poisson kernel. The Riemann mapping theorem. The prime number theorem.

This course provides an introduction and exposure to dynamical systems, with particular emphasis on low-dimensional systems such as interval maps and maps of the plane. Through these simple models, students will become acquainted with the mathematical theory of chaos and will explore strange attractors, fractal geometry and the different notions of entropy. The course will focus mainly on examples rather than proofs; students will be encouraged to explore dynamical systems by programming their simulations in Mathematica.

This course will focus on combinatorics. Topics will be selected by the instructor and will vary from year to year.

This course introduces students to combinatorial games, two-player (matrix) games, Nash equilibrium, cooperative games, and multi-player games. Possible additional topics include: repeated (stochastic) games, auctions, voting schemes and Arrow's paradox. Numerous examples will be analyzed in depth, to offer insight into the mathematical theory and its relation to real-life situations.

Manifolds, vector fields, tangent spaces, vector bundles, differential forms, integration on manifolds.

A significant project in any area of mathematics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a mathematics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken.

A significant project in any area of mathematics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a mathematics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken.

Independent study under direction of a faculty member.

Independent study under direction of a faculty member.

Students will learn and practice a variety of techniques relating to orchestral and choral composition and arranging. Essential concepts relating to clefs and pitch range will be taught, as well as compositional principles and techniques such as voice leading and counterpoint. An emphasis will be placed on honing creativity and applying a variety of non-Western musical influences. Students will be able to apply the material learned in this course to all other courses relating to music creation.

Students will apply concepts learned during the first two years of the program to the creation and performance of advanced multi-part vocal arrangements. A variety of methods of vocal arranging will be explored, and performance techniques such as balancing, diction, breath control, projection, and dynamics will be applied to the execution of the created arrangements.

In this course students explore a variety of topics relating to songwriting. Advanced techniques relating to melody, lyric, and chord writing will be discussed and applied creatively to original songs. This course is taught at Centennial College.

This course will prepare students to become professional performers that meet and exceed audience expectations. From the perspective of an "indie" musician, students will learn how to perform in line with contemporary standards of excellence and entertainment.

This course will introduce students to live and studio sound by giving them hands-on experience on equipment in a professional recording studio. This course is taught at Centennial College.

Students will develop a foundational knowledge of the music industry that will serve as a base for all other music business-related courses. Students will be introduced to the terminology, history, infrastructure, and careers of the music industry. Students will be introduced to fundamental areas of business management. Legal issues and the future of the music industry will also be discussed. All material will be taught from a uniquely Canadian perspective.

Students will learn how to earn a sustainable full-time living as a self-employed musician and creative professional. Topics covered include grant writing, publishing, licensing, contracts, and copyright. Students will also learn some basic accounting and marketing skills. The course will provide students with a foundation for courses in the Music Creation and Business track and for the pursuit of a music career.

Students will learn how to apply principles and values relating to global citizenship and equity to the music industry. Issues relating to women, visible minorities, and members of the LBGT+ community in the music industry will be explored as students consider ways they can act as catalysts for positive change. Students will also learn about recent and upcoming political, economic, social and technological changes that affect the music industry of the present and future.

This course will train students for the role of live sound engineer. Students will learn how to setup, operate, take down, maintain, and store all components of a live sound system. Other topics to be discussed include acoustics, sound tests, working with performers, and career options.

This course focuses specifically on sound mixing and editing – all stages of post-production. Students will learn how to work efficiently with a variety of different musical content. This course will help students with regard to software proficiency, and to develop a producer's ear. This course is taught at Centennial College.

This course focuses on a variety of techniques for achieving the best possible sound quality during the sound recording process. Topics discussed include acoustics, microphone selection and placement, drum tuning, guitar and bass amplifiers, preamplifiers, and dynamics processors. This course will help prepare students for work as recording studio engineers, and to be self-sufficient when outputting recorded works as a composer/musician. This course is taught at Centennial College.

Students will learn how to successfully run a professional recording studio session by assuming a leadership role as audio engineer and producer, and by synthesizing techniques relating to audio production and recording, audio mixing and editing, and audio consoles. This experiential course will also provide opportunities for students to exercise and develop troubleshooting and critical thinking skills that are necessary in a recording studio. Students will also learn about studio equipment and maintenance in ways that build on prior courses.

Students will explore a variety of techniques associated with creating a professional mastered stereo mix. Students will learn how to use various digital and analog tools during the mastering process in order to create final stereo mixes that reflect industry practices and standards.

Students will learn how to mix audio for projects associated with video games and virtual reality (VR). Students will explore techniques for recording sound that accompanies video filmed by a 360-degree camera, and how to effectively use a variety of software programs and tools associated with gaming and VR.