This course will cover primarily the theory and applications of differential calculus, before finishing with an introduction to integral calculus. This course is designed to ensure that all students are equally prepared for further calculus studies. Depending on where you completed your high school mathematics studies, topics in this course may be review or they may be new content and thus this course is a good opportunity to fill in any gaps in mathematical knowledge and skills.
Prerequisites: SC/MATH 1520 3.00, or 12U Calculus and Vectors (MCV4U) or equivalent.
Course credit exclusions: SC/MATH 1300 3.00, SC/MATH 1505 6.00, SC/MATH 1530 3.00, SC/MATH 1550 6.00, GL/MATH/MODR 1930 3.00, AP/ECON 1530 3.00, SC/ISCI 1401 3.00 and SC/ISCI 1410 6.00.
Note: This course is a prerequisite for SC/MATH 1014 3.00 and SC/MATH 1310 3.00.
This course will cover primarily the theory and applications of integral calculus, before finishing with an introduction to infinite sequences and series. This course is designed to ensure that all students are equally prepared to apply this content in their chosen field. For most students, the content in this course will be new and a strong foundation in MATH 1013 is essential for success.
Prerequisite(s): One of SC/MATH 1013 3.00, SC/MATH 1300 3.00, GL/MATH 1901 3.00, or SC/ISCI 1401 3.00; for non-science students only, six credits from SC/MATH 1530 3.00 and SC/MATH 1540 3.00, SC/MATH 1550 6.00, AP/ECON 1530 3.00 and AP/ECON 1540 3.00.
Course credit exclusions: SC/MATH 1310 3.00, SC/MATH 1505 6.00, GL/MATH/MODR 1940 3.00, SC/ISCI 1402 3.00, SC/ISCI 1410 6.00.
Note: This course is a prerequisite for SC/MATH 2015 3.00, SC/MATH 2030 3.00, SC/MATH 2041 3.00, SC/MATH 2280 3.00, SC/MATH 2310 3.00, SC/MATH 2930 3.00 and SC/MATH 3241 3.00.
Cross listed to: LE/EECS 1019 3.00
The purpose of this course is to develop students' ability to think abstractly, develop and use precise formulations of mathematical ideas, and prepare students for more advanced topics in mathematics and computer science. Discrete mathematics is the study of discrete structures like sets, functions, relations, graphs, and trees, and the relationships between them. An example of a problem solved using discrete mathematics is “What is the shortest path between two cities using a transportation system?” Solving this problem involves constructing a graph, and will not be simply solved by applying a formula. Discrete mathematics will challenge you and make you use your brain in ways that other courses have not because one of the primary goals of this course is to teach mathematical reasoning and problem solving, rather than, giving formulae, and a set of skills to apply these formulae. By the end of this course, you will be able to (a) Apply logical arguments, definitions and set identities to write valid proofs using a variety of methods; (b) Compare functions in terms of their structure and growth by proving properties of given functions (e.g. one-to-one, onto, big-O, big-Omega, big-Theta); (c) Prove properties of recursively defined structures and solve counting problems and recurrence relations; and (d) Analyze graphs to determine the properties they have (e.g. type of graph, connectivity, Euler and Hamilton paths and circuits, etc.)
Prerequisite(s): SC/MATH 1190 3.00, or two 4U Math courses, including MHF4U (Advanced Function).
Course credit exclusions: LE/EECS 1028 3.00, SC/MATH 1028 3.00, SC/MATH 2320 3.00.
Note: SC/MATH 1019 3.00 is a prerequisite for SC/MATH 1090 3.00 and MATH 3021 3.00.
Linear algebra is the mathematics of vectors, matrices, and linear transformations. These concepts are a common theme throughout mathematics with several applications including statistics, linear programming, computer graphics, business and industry, and quantum mechanics to name but a few. In this introductory course in linear algebra, students will learn to solve systems of linear equations, the structures of vectors in real Euclidean spaces including bases and dimension, algebraic properties of matrices, linear transforms on real Euclidean spaces, determinants, and real eigenvectors. This course is taught at a higher level than MATH 1025 with an emphasizes on mathematical reasoning and proofs.
Prerequisite: 12U Advanced Functions (MHF4U) or equivalent.
Course credit exclusions: SC/MATH 1025 3.00, SC/MATH 2221 3.00, GL/MATH/MODR 2650 3.00.
Note: This course is a prerequisite for SC/MATH 2022 3.00, SC/MATH 2200 3.00, SC/MATH 2270 3.00, SC/MATH 3141 3.00, SC/MATH 3171 3.00, SC/MATH 3172 3.00, SC/MATH 3241 3.00, SC/MATH 3330 3.00 and SC/MATH 4171 3.00.
This course gives a one-term intensive introduction to linear algebra, with emphasis on its applications. This course is particularly appropriate for students taking Science or Engineering programs which require one term’s worth of linear algebra. Topics include: systems of linear equations, matrices and matrix algebra, applications of matrices, determinants, vector space concepts for Euclidean n-space (e.g. basis, dimension and linear transformations), eigenvalues and eigenvectors, applications of eigenvalues and eigenvectors, complex numbers.
Prerequisite: 12U Advanced functions (MHF4U) or equivalent.
Course credit exclusions: SC/MATH 1021 3.00, SC/MATH 2221 3.00, GL/MATH/MODR 2650 3.00.
Note: This course is a prerequisite for SC/MATH 2270 3.00, SC/MATH 2271 3.00, SC/MATH 2930 3.00, SC/MATH 3141 3.00, SC/MATH 3171 3.00, SC/MATH 3241 3.00, SC/MATH 3330 3.00 and SC/MATH 4171 3.00.
Cross listed to: LE/EECS 1028 3.00
An introduction to propositional logic and application to switching circuits; sets, relations and functions; predicate logic and proof techniques; induction with applications to program correctness; basic counting techniques with applications; graphs and trees with applications in circuit analysis, information storage and retrieval, Huffman coding; automata and applications in software engineering.
Prerequisites: MHF4U (Advanced Function) and MCV4U (Calculus and Vectors).
Course Credit exclusions: LE/CSE 1019 3.00 (prior to Fall 2014), LE/EECS 1019 3.00, SC/CSE 1019 3.00 (prior to Summer 2013), SC/MATH 1019 3.00, SC/MATH 2320 3.00.
By taking this course, students will be able to master the syntax and proof techniques of propositional and predicate logic, as well as their informal semantics. The proper understanding of propositional logic is fundamental to all levels of computer programming, even the most basic, while the ability to correctly use variables, scope and quantifiers is crucial in the use of loops, subroutines, and modules, and in software design. Logic is used in many areas of computer science, including digital design, program verification, databases, artificial intelligence, computability and complexity, algorithm analysis, and software specification. Every program implicitly asserts a theorem to the effect that the program will do what its documentation says it will. Proving that theorem is not merely a matter of luck or patient debugging. Making a correct program can be greatly aided by a logical analysis of what it is supposed to do, and, for small pieces of code, a proof that the code works can be produced hand‑in‑hand with the construction of the code itself.
Prerequisite: SC/MATH 1190 3.00 or SC/MATH 1019 3.00.
Course credit exclusion: SC/MATH 4290 3.00.
Statistics is the science of data, and this course will introduce you to some of the basic, yet incredibly useful, statistical techniques. Topics include graphical and numerical method of summarizing both univariate and bivariate data, random variables and probability distributions, sampling variability and sampling distributions, estimation and testing using a single sample. We will consider comparison of two populations and/or linear regression if time permits. It is recommended that students have at least one OAC in mathematics or a 12U mathematics course. Although students might be making use of the computer to calculate statistics, no previous experience in computing is required. Students will receive all the necessary instruction about how to use the statistical computer package chosen by the instructor. Although this course is recommended for students who wish to major in statistics, the concepts are broadly applicable and it should be interesting to students who do not plan to specialize in statistics.
Prerequisite: At least one 12U mathematics course or equivalent is recommended.
Course credit exclusion: SC/MATH 2560 3.00, SC/MATH 2930 3.00, GL/MATH/MODR 1610 3.00, SC/BIOL 2060 3.00.
Note: This course is a prerequisite for SC/MATH 2131 3.00, SC/MATH 3330 3.00, SC/MATH 3333 3.00 and SC/MATH 4143 3.00.
This course is an introduction to discrete mathematics. The topics covered are widely used throughout mathematics; many will crop up again in other mathematics courses. The purpose of this course is to give these topics a thorough treatment early in a student’s mathematical studies, with the intention of enhancing his or her understanding of future courses, irrespective of whether those courses have MATH 1190 as a prerequisite. The emphasis will be on understanding the basic ideas, and developing an appreciation for mathematical reasoning, proofs and problem solving.
There is considerable overlap between the topics of MATH 1190 and those of the course MATH 1019 (see the MATH 1019 entry earlier in this supplemental calendar). Math majors can choose to take either of these two courses (see the Mathematics BA, BSc program tables at the back of this supplemental calendar), but, before choosing, they should note that: The coverage of topics in MATH 1019 should be more in-depth and perhaps at a faster pace than in MATH 1190.
Prerequisite: Advanced Functions (MHF4U) or equivalent, or SC/MATH 1510 6.00, or GL/MATH 1670 6.00 or SC/MATH 1710 6.00.
Course credit exclusion: GL/CSLA/MATH/MODR 1650 3.00.
Notes:
- This course may not be taken for degree credit by any student who has passed SC/MATH 1019 3.00 or any 3000- or higher-level mathematics course.
- This course is a prerequisite for SC/MATH 1019 3.00, SC/MATH 1090 3.00 and SC/MATH 3021 3.00.
Most high school mathematics problems are solved using algorithmic methods or by reference to model solutions. The main purpose of this course is to develop students' critical thinking abilities in order to obtain the confidence and ability to attack richer and more demanding problems. This is accomplished by developing logical and rational thinking through the mathematical languages of problems, proofs, and conjectures.
The attempt to verify the correctness of one’s work leads to the need to explain one’s work to others. Learning how to present convincing reasoning as proof is a major goal of this course. Thus there will be great emphasis on the communication of convincing argument and significant class time will be devoted to reading, writing, and discussing proofs and mathematical arguments. Students will learn that theorems can often be correctly proved by many different approaches and that some approaches may offer advantages over others. Students will also learn that some proposed proofs have gaps that can be fixed using additional argument. Class and tutorial attendance is mandatory and active participation is expected of all students. Students will learn the mathematical word-processing package LaTeX, which will be required for homework assignments.
Prerequisite: 12U Advanced Functions (MHF4U) or equivalent.
Course credit exclusion: SC/MATH 2200 3.00.
Notes:
- Not open to any student who is taking or has passed a MATH course at the 3000 level or higher.
- This course is a prerequisite for SC/MATH 2001 3.00, SC/MATH 3021 3.00 and SC/MATH 3141 3.00.
This course deals with the notion of risk and the ways to manage it, by exploring the general framework of risk management for businesses, individuals and societies, and by focusing on the role of insurance as a risk transfer mechanism. More specifically, the course categorizes and studies those risks that are associated with financial markets (liquidity risk, pricing risk, credit risk, among other financial risks) as well as those risks that arise from operations of an enterprise, regulations, digital transformation, the impacts of the environment or a catastrophe (among other non-financial risks). Also, the course examines in detail the various aspects of the insurance mechanism as a route to manage some of the aforementioned risks. The course combines classical lectures with biweekly presentations by visiting risk professionals, thus immersing the students into theory and practice of modern risk management.
Prerequisite: None.
Differential calculus is the study of rates of change of real valued functions. This notion will be precisely defined and key facts about it will be proved. The examination of these concepts will entail a close study of limits and continuity and will culminate with the proof of a remarkable theorem about the rate of change of the area bounded by the graph of a function. This is a theoretical course emphasizing precise definitions and featuring proofs of some important results. Students successfully completing this course should be well prepared to continue their studies of more advanced courses such as MATH 2001. We recommend this course for math majors and computer science students.
Prerequisite: SC/MATH 1520 3.00 or SC/MATH 1710 6.00, or 12U Calculus and Vectors (MCV4U) or equivalent.
Course credit exclusions: SC/MATH 1013 3.00, SC/MATH 1505 6.00, SC/MATH 1530 3.00, SC/MATH 1550 6.00, GL/MATH/MODR 1930 3.00, AP/ECON 1530 3.00; SC/ISCI 1401 3.00, SC/ISCI 1410 6.00.
Note: This course is a prerequisite for SC/MATH 1014 3.00, SC/MATH 1310 3.00, SC/MATH 2001 3.00 and SC/MATH 2200 3.00.
This is the second in a series of introductory calculus courses designed to follow MATH 1300. The study of integral calculus begun in MATH 1300 is continued. Exponential and logarithmic functions are properly defined using integrals. Methods of integration are discussed. Applications are made to compute volumes, approximate areas and distance travelled. Improper integrals are used to study unbounded areas. A precise definition for adding up infinitely many numbers will be given and some of the many applications of this concept will be examined. This is a theoretical course emphasizing precise definitions and featuring proofs of some important results. Students successfully completing this course should be well prepared to continue their studies of more advanced courses such as MATH 2001. We recommend this course for math majors and computer science students.
Prerequisite(s): One of SC/MATH 1013 3.00, SC/MATH 1300 3.00, GL/MATH 1901, SC/ISCI 1401 3.00; for non-science students only, six credits from SC/MATH 1530 3.00 and SC/MATH 1540 3.00, SC/MATH 1550 6.00, AP/ECON 1530 3.00 and AP/ECON 1540 3.00.
Course credit exclusions: SC/MATH 1014 3.00, SC/MATH 1505 6.00, GL/MATH/MODR 1940 3.00, SC/ISCI 1402 3.00, SC/ISCI 1410 6.00.
Notes: This course is a prerequisite for SC/MATH 2015 3.00, SC/MATH 2030 3.00, SC/MATH 2041 3.00, SC/MATH 2200 3.00, SC/MATH 2280 3.00, SC/MATH 2310 3.00, SC/MATH 30013.00 and SC/MATH 3241 3.00.
The course content emphasizes the following topics in an introductory but mathematically rigorous way: systems of linear equations, functions, differentiation and differentials with an emphasis on applications in the life sciences where possible.
Having a strong foundation in secondary school level algebra is necessary for success in this course, and students who feel that they do not have that foundation are strongly encouraged to enroll in Math 1510 first to build their foundational mathematics. Any student that gets a B or higher in Math 1510 should be prepared for Math 1506.
Students enrolled in Math 1506 take an assessment quiz in the first week of the course, and if a student does poorly on the quiz it is strongly recommended they drop the course and enroll in Math 1510. Math 1506 is designed for students enrolled in programs that only require 6 credits of mathematics, and should be taken in the first year of academic studies. Typically, students in a Biology, Psychology or Kinesiology enroll in Math 1506. Students who are looking for a comprehensive study of the topics listed above should not be taking Math 1506. The mathematics learned in Math 1506 will not be sufficient for students furthering a pursuit of mathematics at an intermediate or advance level.
Prerequisite: 12U Advanced Functions (MHF4U) or equivalent, or SC/MATH 1510 3.00.
Course Credit exclusions: SC/MATH 1013 3.00, SC/MATH 1300 3.00, SC/MATH 1530 3.00, SC/MATH 1550 6.00, GL/MATH/MODR 1930 3.00, AP/ECON 1530 3.00, SC/ISCI 1401 3.00, SC/ISCI 1410 6.00, SC/MATH 1505 6.00.
Note: This course is a prerequisite for SC/MATH 1507 3.00.
Math 1507 is a continuation of the material in Math 1506 and the content emphasizes the following topics in an introductory but mathematically rigorous way: integration, probability and an introduction to statistics with applications to the life sciences where possible. Math 1507 is designed for students enrolled in programs that only require 6 credits of mathematics, and should be taken in the first year of academic studies. Typically, students in a Biology, Psychology and/or Health program enroll in Math 1507. Students who are looking for a comprehensive study of the topics listed above should not be taking Math 1507. The mathematics learned in Math 1507 will not be sufficient for students furthering a pursuit of mathematics at an intermediate or advance level.
Prerequisite: SC/MATH 1506 3.00.
Course Credit exclusions: SC/MATH 1014 3.00, SC/MATH 1310 3.00, SC/MATH 1540 3.00, SC/MATH 1550 6.00, GL/MATH/MODR 1940 3.00, AP/ECON 1540, SC/ISCI 1402 3.00, SC/ISCI 1410 6.00, SC/MATH 1505 6.00.
This course is intended for students who wish to strengthen their knowledge in high school mathematics as preparation for university level mathematics courses, such as SC/MATH 1506 3.00 and SC/MATH 1520 3.00. Topics include algebraic equations and inequalities; simple sequences and series; analytic geometry; trigonometry; functions, including algebraic, exponential, logarithmic and trigonometric functions.
Prerequisites: 11U Functions.
Course credit exclusions: SC/MATH 1710 6.00, GL/ITEC/MATH/MODR 1670 6.00.
Notes:
- This course may not be taken by any student who has taken or is currently taking another university course in mathematics or statistics including ECON 1530 3.00 and ECON 1540 3.00, except for SC/MATH 1520 3.00.
- This course is a prerequisite for SC/MATH 1506 3.00
This course is required for BASc in Computer Science for Software Development (CSSD) and BASc Honours in Digital Technologies (DT). It covers general mathematics for students who major in software development. More precisely, students learn introductory and fundamental topics from broad areas of mathematics. It is expected that students will learn more advanced and/or specialized subjects through just-in-time learning as necessity arises.
Prerequisites: 12U Advanced Functions (MHF4U) or equivalent, or SC/MATH 1510 3.00.
Course credit exclusions:
Notes:
- This course may not be taken by any student who has taken or is currently taking another university course in mathematics or statistics except MATH 1510.
This course covers the elements of differential calculus including limits, rates of changes, derivatives, methods of differentiation, applications of derivatives, related rates, extreme values, maximum and minimum problems and curve sketching. The course also covers elements of vectors in 2- and 3-space including dot products, cross products, lines, and planes.
Prerequisite: One of: MATH 1510 6.00, GL/MATH 1670, 12U Advanced Functions (MHF4U) or equivalent, or permission of the department.
Notes:
- This course may be taken at the same time as the second half of SC/MATH 1510 6.00.
- This course may not be taken by any student who has passed or is currently taking another university course in calculus or AP/ECON 1530 3.00 or AP/ECON 1540 3.00.
- This course is a prerequisite for SC/MATH 1013 3.00 and SC/MATH 1300 3.00.
This course is an introduction to statistics specifically designed for students in the Business and Society program in the Division of Social Science. Students learn basic and practical statistical techniques to explore and analyze data. Emphasis is placed on statistical reasoning and the critical interpretation of statistical information such as that seen in the media and in journals.
There is also a strong emphasis on acquiring practical skills in data exploration with spreadsheet software such as Excel or Calc. The course includes weekly tutorials in a computer lab.
Course credit exclusions: SC/NATS 1500 3.00.
Note: This course may not be taken for credit by any student who has successfully completed or is concurrently enrolled in SC/MATH 1131 3.00, SC/MATH 2565 3.00, SC/MATH 2560 3.00, SC/ MATH 2570 3.00, SC/MATH 2930 3.00, SC/BIOL 2060 3.00 or equivalents.
Introduction to interest rates and the time value of money. Topics include simple and compound interest, equations of value, annuities, loans, mortgages, and bonds. A different title for this course might be “The Mathematics of Money”. As money moves through time, the force of interest must be taken into account. Doing so requires mathematical calculations, and this course introduces some of those calculations. This course will be offered in both Fall term and Winter term. It should be particularly attractive to students in the Business and Society Program, and also to students in economics and business-related areas. The course emphasizes problem-solving rather than theory. Spreadsheets (e.g. Excel/Open Office/Google Sheets) will be taught and used extensively. The grading scheme for the course has not been determined, but it will likely involve one or two tests and a final examination.
Prerequisite: Ontario Grade 12 Advanced Functions or equivalent.
Course credit exclusion: SC/MATH 2580 6.00 (prior to Fall 2010), SC/MATH 2280 3.00, GL/ECON1950 3.00, GL/MATH 1950 3.00, GL/MATH 2680 6.00, GL/MODR 1950 3.00.
Note: This course is a prerequisite for SC/MATH 2581 3.00.