Note: This is the 2011–2012 edition of the eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or click here to jump to the newest eCalendar.
Program Requirements
The Concurrent Bachelor of Science (B.Sc.) and Bachelor of Education (B.Ed.)  Major Mathematics for Teachers is jointly offered by the Faculty of Science and the Faculty of Education. Separately, the Bachelor of Science degree requires 90 credits (or 120 credits for students who have not completed the basic sciences) and the Bachelor of Education degree requires 120 credits. In the concurrent program, the requirements for the two degrees are combined in such a way that students complete 135 (or 165 credits) to fulfil all the requirements for graduation for both the B.Sc. and the B.Ed. Graduates of the B.Ed. degree are recommended by the University to the Quebec Ministère de l'Éducation, du Loisir et du Sport (MELS) for Quebec Teacher Certification. For more information about teacher certification in Quebec, please refer to the Faculty of Education section under "Overview of Faculty Programs", "Undergraduate Education Programs", and "Quebec Teacher Certification". The Major Mathematics is one of the nine variations of the program and allows students to focus their Science degree in Mathematics.To fulfil the requirements for graduation for the Concurrent Bachelor of Science and Bachelor of Education, the 135 credits (or 165 credits for students admitted without basic sciences) include the following:
(30 credits of Science Freshman Program (for students admitted without basic sciences))
60 credits of Education Component
54 credits of Science Component consisting of:
 54 credits of the Major Mathematics
21 credits of Electives, of which at least 18 credits must be Science Electives, depending on how many credits count toward both the B.Sc. and the B.Ed. degrees.
For details on the counting of credits toward both degrees (doublecounting) visit the program website http://www.mcgill.ca/scienceforteachers/.
B.Sc. Freshman Program
Students who enter Science in U0 will normally be registered in the Science Freshman Program until they complete their first year. They must consult an adviser in the Science Office for Undergraduate Student Advising (SOUSA) to obtain advice and approval of their course selection. Full details are available on the SOUSA website at http://www.mcgill.ca/science/sousa. Academic advising is also available by email. The address is newstudentadvising.science [at] mcgill.ca.
Students normally complete 30 credits which must include at least seven courses from the list of Approved Freshman Science Courses, selected as follows:
General Math and Science Breadth
Six of the Freshman courses must satisfy one of the following:
Option 1) 2 courses from MATH and 4 courses from BIOL, CHEM or PHYS;
or
Option 2) 3 courses from MATH and 3 courses from BIOL, CHEM or PHYS.
Science Complementary
The seventh course is chosen from the list of Approved Freshman Science Courses.
Notes:
1. Students who have not studied all of Biology, Chemistry, and Physics at the grade 12 level or equivalent are strongly advised to include at least one course in the missing discipline in their Freshman Program.
2. Many students will complete more than seven courses from the Approved Freshman Science Courses list, particularly those who wish to leave several options open for their choice of major.
3. Students entering the Freshman Program must be aware of the department specific requirements when selecting their courses. Detailed advising information is available at http://www.mcgill.ca/science/sousa/new_students/u0/bsc_freshman/specific/.
4. The maximum number of courses per term, required, complementary, and elective, is five.
List of Approved Freshman Science Courses
Select the approved courses according to the instructions above.
Note:
* CHEM 115 (not open to students who are taking or have taken CHEM 110 or CHEM 120)
* CHEM 120 (not open to students who have taken CHEM 115)

BIOL 111 Principles: Organismal Biology (3 credits)
Overview
Biology (Sci) : An introduction to the phylogeny, structure, function and adaptation of unicellular organisms, plants and animals in the biosphere.
Terms: Fall 2011
Instructors: Irene GregoryEaves, Andrew Hendry, Suzanne Gray (Fall)
Fall
2 hours lecture and 3 hours laboratory
Restriction: Not open to students who have taken CEGEP objective 00UK or equivalent; or BIOL 115.
This course serves as an alternative to CEGEP objective code 00UK
May require departmental approval.
Open to all students wishing introductory biology.
Attendance at first lab is mandatory to confirm registration in the course.
This class will use a Student Response System (clicker) which can be obtained from the Bookstore.

BIOL 112 Cell and Molecular Biology (3 credits)
Overview
Biology (Sci) : The cell: ultrastructure, division, chemical constituents and reactions. Bioenergetics: photosynthesis and respiration. Principles of genetics, the molecular basis of inheritance and biotechnology.
Terms: Winter 2012
Instructors: Joseph Alan Dent, Frieder Schöck (Winter)

CHEM 110 General Chemistry 1 (4 credits)
Overview
Chemistry : A study of the fundamental principles of atomic structure, radiation and nuclear chemistry, valence theory, coordination chemistry, and the periodic table.
Terms: Fall 2011
Instructors: JeanMarc Gauthier, Ashok K Kakkar, Bryan Clifford Sanctuary, Ariel Fenster (Fall)
Fall
Prerequisites/corequisites: College level mathematics and physics or permission of instructor; CHEM 120 is not a prerequisite
Each lab section is limited enrolment

CHEM 115 Accelerated General Chemistry: Giants in Science (4 credits) *
Overview
Chemistry : An advanced combined version of CHEM 110 and CHEM 120 that will emphasize developments in the chemical sciences that changed the way nature was understood, focusing, where possible, on examples that led to Nobel Prizes.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.
 Fall
 Prerequisite: Grade 12 Chemistry
 Corequisites: PHYS 131 and MATH 140 or MATH 150
 Restrictions: Enrolment is restricted to students who have obtained a grade greater than 95% in their high school university preparatory chemistry course (e.g., the Ontario Grade 12 University Preparation Chemistry Course [SCH4U]). Not open to students who are taking or have taken CHEM 110 or CHEM 120.
 Note: CHEM 115 and (CHEM 110 plus CHEM 120) are considered equivalent from a prerequisite point of view. If you are planning on applying to medical school, note that some medical schools require applicants to have two general chemistry courses; at McGill you would have to take an additional physical chemistry course like CHEM 204 or equivalent to meet this requirement.

CHEM 120 General Chemistry 2 (4 credits) *
Overview
Chemistry : A study of the fundamental principles of physical chemistry.
Terms: Winter 2012
Instructors: Ariel Fenster, Ian Sydney Butler, Bradley Siwick, JeanMarc Gauthier (Winter)
Winter
Prerequisites/corequisites: College level mathematics and physics, or permission of instructor: CHEM 110 is not a prerequisite
Each lab section is limited enrolment

COMP 202 Foundations of Programming (3 credits)
Overview
Computer Science (Sci) : Introduction to programming in a modern highlevel language, modular software design and debugging. Programming concepts are illustrated using a variety of application areas.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Daniel Pomerantz, Jorg Andreas Kienzle (Fall) Daniel Pomerantz, Xue Liu (Winter) Daniel Pomerantz (Summer)
3 hours
Prerequisite: a CEGEP level mathematics course
Restrictions: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computation. COMP 202 cannot be taken for credit with or after COMP 250

ESYS 104 The Earth System (3 credits)
Overview
Earth System Science : Earth system science examines the complex interactions among the atmosphere, biosphere, geosphere and hydrosphere. It focuses on physical, chemical, and biological processes that extend over spatial scales ranging from microns to the size of planetary orbits, and spans time scales from fractions of a second to billions of years.
Terms: Winter 2012
Instructors: William Minarik, Frederic Fabry (Winter)

MATH 133 Linear Algebra and Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases; quadratic loci in two and three dimensions.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Shabnam Akhtari, Djivede Kelome, William J Anderson, Adam Clay, Sidney Trudeau (Fall) Djivede Kelome, Wilbur Jonsson (Winter) Nabil Kahouadji (Summer)
3 hours lecture, 1 hour tutorial
Prerequisite: a course in functions
Restriction: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
Restriction Note B: Not open to students who have taken or are taking MATH 123, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.

PSYC 100 Introduction to Psychology (3 credits)
Overview
Psychology : Introduction to the scientific study of mind and behavior, including basic concepts and methods in psychology while also highlighting the relevance of psychology to everyday life; attachment, aggression, depression, parenting and personality change.
Terms: Fall 2011, Summer 2012
Instructors: James C MacDougall (Fall) Jens Pruessner (Summer)
Fall
2 lectures; 1 conference
Restriction: Not open to students who have passed an Introductory Psychology course in CEGEP: 350101 or 350102 or equivalent
First calculus course, one of:

MATH 139 Calculus 1 with Precalculus (4 credits)
Overview
Mathematics & Statistics (Sci) : Review of trigonometry and other Precalculus topics. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Terms: Fall 2011
Instructors: Axel W Hundemer (Fall)
Fall
4 hours lecture, 1 hour tutorial
Prerequisite: a course in functions
Restriction: Not open to students who have taken CEGEP objective 00UN or equivalent.
Restriction Note B: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics.
Students continue in MATH 141
Each Tutorial section is enrolment limited

MATH 140 Calculus 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Stephen W Drury, David Shirokoff, Mark Eric Fels (Fall) Wilbur Jonsson (Winter) Yaiza Canzani Garcia (Summer)
3 hours lecture, 1 hour tutorial
Prerequisite: High School Calculus
Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
Restriction: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
Each Tutorial section is enrolment limited

MATH 150 Calculus A (4 credits)
Overview
Mathematics & Statistics (Sci) : Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
Terms: Fall 2011
Instructors: Charles Roth (Fall)
Fall
3 hours lecture, 2 hours tutorial
Students with no prior exposure to vector geometry are advised to take MATH 133 concurrently. Intended for students with high school calculus who have not received six advanced placement credits
Restriction: Not open to students who have taken CEGEP objective 00UN or equivalent
Restriction Note B: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222
Second calculus course, one of:

MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Sungmo Kang (Fall) Antonio Lei, Stephen W Drury, Layan El Hajj (Winter) Hadi Bigdely, Philip Grech (Summer)
Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent
Restriction Note B: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Each Tutorial section is enrolment limited

MATH 151 Calculus B (4 credits)
Overview
Mathematics & Statistics (Sci) : Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
Terms: Winter 2012
Instructors: Charles Roth (Winter)
Winter
3 hours lecture; 2 hours tutorial
Each Tutorial section is enrolment limited
Prerequisite: MATH 150
Restriction: Not open to students who have taken CEGEP objective 00UP or equivalent
Restriction: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
Restriction: Not open to students who have taken MATH 152
First physics course, one of:

PHYS 101 Introductory Physics  Mechanics (4 credits)
Overview
Physics : An introductory course in physics without calculus, covering mechanics (kinematics, dynamics, energy, and rotational motion), oscillations and waves, sound, light, and geometrical optics.
Terms: Fall 2011
Instructors: Kenneth J Ragan (Fall)
Fall
3 hours lectures; 2 hours laboratory; tutorial sessions
Restriction: Not open to students taking or having taken PHYS 131, CEGEP objective 00UR or equivalent
Laboratory sections have limited enrolment

PHYS 131 Mechanics and Waves (4 credits)
Overview
Physics : The basic laws and principles of Newtonian mechanics; oscillations and waves.
Terms: Fall 2011
Instructors: Kenneth J Ragan, Edith M Engelberg (Fall)
Second physics course, one of:

PHYS 102 Introductory Physics  Electromagnetism (4 credits)
Overview
Physics : Electric field and potential. D.C. circuits and measurements. Capacitance. Magnetic field and induction. A.C. circuits Semiconductor devices and their application. Electromagnetic waves.
Terms: Winter 2012
Instructors: Zaven Altounian (Winter)

PHYS 142 Electromagnetism and Optics (4 credits)
Overview
Physics : The basic laws of electricity and magnetism; geometrical and physical optics.
Terms: Winter 2012
Instructors: Yoichi Miyahara (Winter)
Winter
3 hours lectures, 3 hours laboratory in alternate weeks; tutorial sessions
Prerequisite: PHYS 131.
Corequisite: MATH 141 or higher level calculus course.
Restriction: Not open to students taking or having taken PHYS 102, CEGEP objective 00UR or equivalent
Laboratory sections have limited enrolment
Electives
Students wishing to take elective courses may choose them from introductory courses offered by departments in the Faculties of Science or of Arts. A list of recommended courses is found at http://www.mcgill.ca/science/sousa/new_students/u0/bsc_freshman/approved/. Certain courses offered by other faculties may also be taken, but some restrictions apply.
Consult the SOUSA website at http://www.mcgill.ca/science/sousa/continuing_students/bsc/outside/ for more information about taking courses from other faculties.
Education Component (60 credits)
60 credits of Education Component, consisting of:
54 credits of required courses
6 credits of complementary courses
Required Courses
54 credits
* Note: The courses marked with an asterisk are counted toward both degrees. They will count as "electives" for the B.Sc. degree, although a grade of "C" or better is required.
The English Language Requirement (EDEC 215) must be taken in the Fall semester following the Freshman year.

EDEC 201 First Year Professional Seminar (1 credit)
Overview
Curriculum and Instruction : Orientation to the culture and community of school and to teaching as a profession. Focus on the general functioning of schools and complexity of the teacher role. Competencies and working professional portfolios will be addressed.
Terms: Fall 2011, Summer 2012
Instructors: Caroline Joan Riches, Helen Amoriggi, Fiona J Benson, Norman Horner, Rania Delis, Tina Ottoni, Ginette Clarke, Anjali Anna Abraham, Jan Edith Langelier (Fall) Helen Amoriggi, Anila Asghar (Summer)
Corequisite: EDFE 200
Restriction: Open to B.Ed. Secondary and B.Ed. K/Elem. students only

EDEC 215 English Language Requirement
Overview
Curriculum and Instruction : This English Exam for Teacher Certification is a MELS requirement for teaching in the Quebec English school system. Consists of a 2hour exam designed to assess teacher candidates' competency in the language of instruction. Must be completed before the 3rd Field Experience. Students are permitted four attempts to pass. Students who do not pass after four attempts must withdraw from the teacher preparation program.
Terms: Fall 2011, Summer 2012
Instructors: Beverly Anne Baker (Fall) Beverly Anne Baker (Summer)

EDEC 247 Policy Issues in Quebec Education (3 credits) *
Overview
Curriculum and Instruction : This course examines the organization of education in Quebec from various perspectives, including historical, political, social and legal. It aims to provide students with sufficient knowledge that they can begin the lifelong learning process of a professional educator, aware of, and contributing to, the policy talk on school.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Tino Bordonaro (Fall) Donal Irving (Winter) Donal Irving (Summer)
Restriction: Not open to students who have taken EDEM 405.

EDEC 254 Second Professional Seminar (Secondary) (1 credit)
Overview
Curriculum and Instruction : Preparation for the second field experience through development of basic practices in planning and teaching in secondary school classrooms. Competencies and professional portfolio will be addressed.
Terms: Summer 2012, Fall 2011, Winter 2012
Instructors: Nicole Marie Bourassa, Ginette Clarke, Jason Lister, Brian Andrew Benoit (Summer) Jason Lister (Fall) Jason Lister (Winter)
Corequisite(s): EDFE 254
Restrictions: Open to B.Ed. Sec and concurrent B.Sc. and B.Ed. students.

EDEC 262 Media, Technology and Education (3 credits) *
Overview
Curriculum and Instruction : Orientation to the equipment and systems of educational technology. Examination of theories of educational technology, media education and technology education and the exploration and development of possible applications in school settings.
Terms: Fall 2011, Winter 2012
Instructors: Lisa Trimble (Fall) Irving Rother, Lisa Trimble (Winter)
Restriction: Not open to students who have taken EDEC 402.

EDEC 351 Third Professional Seminar (Secondary) (2 credits)
Overview
Curriculum and Instruction : Professional portfolios and competencies will be addressed. Preparation for the third field experience through engaging in the full spectrum of unit/lesson planning, critical analysis and selfreflection. Professional portfolios and competencies will be addressed.
Terms: Fall 2011
Instructors: Judy KenworthyGrant, Ginette Clarke (Fall)
Prerequisite: EDEC 254 or EDEC 254D1/D2
Corequisite: EDFE 351
Restriction: Open to B.Ed. Secondary, B.Sc. and B.Ed. concurrent students only. Not open to students who have taken EDEC 306.

EDEC 404 Fourth Year Professional Seminar (Sec) (3 credits)
Overview
Curriculum and Instruction : Preparation for the final field experience and entry into the teaching profession. Emphasis will be placed on developing the ability to demonstrate ethical and responsible professional behaviour in the performance of duties across all professional competencies. Final transition to showcase working professional portfolios will be addressed.
Terms: Winter 2012
Instructors: Jose Manuel Canella, Ginette Clarke, Diane Rinaldis (Winter)

EDES 350 Classroom Practices (Secondary) (3 credits)
Overview
Secondary Education : Competencybased discipline skills and methods of classroom management, emphasizing the relationship between theory and practice; the rationale for various approaches to classroom management; strategies for developing instruction that focus attention and reduce offtask behaviour.
Terms: Fall 2011
Instructors: Norman Horner, Megan Webster, John E Commins, William Keith Wilcox (Fall)

EDES 353 Teaching Secondary Mathematics 1 (3 credits)
Overview
Secondary Education : Directed observations in secondary schools and the study of the general objectives and curriculum trends. The learning problems, teaching strategies and mathematical concepts encountered in the High School curriculum.
Terms: Winter 2012
Instructors: Joanne Malowany (Winter)
Prerequisites: 18 credits in university mathematics courses at or above the 200 level

EDES 453 Teaching Secondary Mathematics 2 (3 credits)
Overview
Secondary Education : This course supplements EDES 353 for students who select Mathematics as a single teachable subject. Evaluation of learning in Mathematics, obstacles to learning, technological aids to learning.
Terms: Winter 2012
Instructors: Terry Wan Jung Lin (Winter)

EDFE 200 First Field Experience (K/Elem & Secondary) (2 credits)
Overview
Student Teaching : Students are assigned to a school for a "participant observer" field experience for a minimum of 10 days.
Terms: Fall 2011, Summer 2012
Instructors: Fiona J Benson (Fall)
Corequisite: EDEC 201
Restriction: Open to B.Ed. Secondary and B.Ed. K/Elem. students

EDFE 254 Second Field Experience (Secondary) (3 credits)
Overview
Student Teaching : A minimum of fifteen days supervised student teaching in a school. Students are expected to apprise themselves of Field Experience 2 expectations and responsibilities as outlined on the Office of Student Teaching website http://www.mcgill.ca/ost/guidelines/.
Terms: Summer 2012, Fall 2011, Winter 2012
Instructors: Fiona J Benson (Fall) Fiona J Benson (Winter)
Corequisite: EDEC 254
Note: Expectations for this field experience, according to your program, can be found at www.mcgill.ca/ost.

EDFE 351 Third Field Experience (Secondary) (8 credits)
Overview
Student Teaching : Supervised student teaching in a school. Students are expected to apprise themselves of Field Experience, dates, duration and responsibilities as outlined on the Office of Student Teaching website http://www.mcgill.ca/ost.
Terms: Fall 2011
Instructors: Fiona J Benson (Fall)
Prerequisites: (EDFE 254 or EDFE 254D1/D2), (EDEC 254 or EDEC 254D1/D2), EDEC 215.
Restriction: Students must have completed, with a grade of C or higher, a minimum of 24 credits in a teachable subject and have taken the corresponding Methods courses as a corequisite.
Note: Expectations for this field experience, according to your program, can be found at www.mcgill.ca/ost.

EDFE 451 Fourth Field Experience (Secondary) (7 credits)
Overview
Student Teaching : A minimum of 35 days of supervised student teaching in a school. Students will be expected to assume a much increased responsibility for student learning, classroom management, and evaluation. Students are expected to apprise themselves of Field Experience 4 expectations and responsibilities as outlined on the Office of Student Teaching website http://www.mcgill.ca/ost/guidelines/.
Terms: Fall 2011, Winter 2012
Instructors: Fiona J Benson (Fall) Fiona J Benson (Winter)
Prerequisites: EDFE 351.
Corequisite: EDEC 404.
Restriction: Open to B.Ed. Secondary students only
Note: Expectations for this field experience, according to your program, can be found at www.mcgill.ca/ost.

EDPE 300 Educational Psychology (3 credits) *
Overview
Ed Psych & Couns (Psychology) : Selected theories, models, and concepts relevant to planning and reflecting upon educational practice and improvement. Overview of development, learning, thinking, motivation, individual difference, etc. In relation to applications in classroom teaching and learning, the complementary role of counsellors and psychologists, educational computing and technology. The Youth Protection Act.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Scott Conrod, Camelia Birlean, Judith Macarthur, Gus Appignanesi, John Ranellucci (Fall) Scott Conrod (Winter) Tara Flanagan, Camelia Birlean (Summer)

EDPE 304 Measurement and Evaluation (3 credits)
Overview
Ed Psych & Couns (Psychology) : The purposes of examinations. Causes of complaints about examinations. Equalizing means and dispersions in distribution of marks. Standardized scores. The percentile system. Essay and objectivetype examinations. Taxonomies of educational objectives. Validity and reliability: item analysis.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Marian Jazvac Martek (Fall) Carlos GomezGaribello (Winter) Marian Jazvac Martek (Summer)

EDPI 309 Exceptional Students (3 credits) *
Overview
Ed Psych & Couns (Inclusive) : Evolution of special education to inclusive education; characteristics, teaching practices, and teachers' roles in inclusive classrooms. Overview of characteristics, causes, needs, and teaching strategies for students with each exceptionality, including students with intellectual, emotional, behavioural, sensory, physical and learning differences.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Maria Di Stasio (Fall) Gus Appignanesi, Ronald William Stringer, Roberta Thomson, Tara Flanagan (Winter) Scott Conrod, Yasaman JalaliKushki (Summer)
Restriction: Open to B.Ed. and Concurrent students only.
Offered through Continuing Education or Summer Studies.

EDPI 341 Instruction in Inclusive Schools (3 credits)
Overview
Ed Psych & Couns (Inclusive) : Planning, implementing and evaluating curriculum and instruction for students with exceptionalities. Using technology and adapting curriculum and instruction for learners with varying abilities, learning styles, and needs. Collaboration with students, families, and other educators in the instructional process. Application component: application of instructional modifications for exceptional students in inclusive schools.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Michael Sornberger, Shannahn McInnis, Casey Finn Lefsrud, Shirely Tolley, Scott Conrod, Karen CohenGazith (Fall) Scott Conrod, Tara Flanagan, David Hoida (Winter) Roberta Thomson, Shannahn McInnis, Judith Macarthur (Summer)
Restriction: Open to B.Ed. students only
Also offered through Continuing Education.
Complementary Courses
6 credits selected as follows:
* Note: The courses marked with an asterisk are counted toward both degrees. They will count as "electives" for the B.Sc. degree, although a grade of "C" or better is required.
3 credits, one of the three following courses:

EDEC 233 First Nations and Inuit Education (3 credits) *
Overview
Curriculum and Instruction : Study of First Nations and Inuit schools as diverse social, cultural, linguistic, political and pedagogical settings. Considers school and community minoritymajority interactions and their influence on teaching and learning in educational settings. Examines how a teacher's personal practice can be influenced by an understanding of these factors.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.

EDEC 248 Multicultural Education (3 credits) *
Overview
Curriculum and Instruction : Introduction to theories about intercultural and multicultural education in Quebec and Canadian schools.
Terms: Fall 2011, Winter 2012
Instructors: Ratna Ghosh, Shaheen Shariff, Mariusz Galczynski (Fall) Jacqueline M Celemencki, Mariusz Galczynski (Winter)

EDEC 249 Global Education and Social Justice (3 credits) *
Overview
Curriculum and Instruction : A crosscurricular, interdisciplinary approach to teaching/creating learning experiences for students. It will foster critical thinking and nurture lifelong global understanding, active engagement and participation in relation to questions of social, economic, and environmental justice, by infusing these issues in the classroom.
Terms: Fall 2011
Instructors: Abdul Aziz Choudry (Fall)
3 credits, one of the two following courses:

EDEC 260 Philosophical Foundations (3 credits) *
Overview
Curriculum and Instruction : Ideas essential for the development of a coherent educational theory and sound professional practice. Reflections on: the nature of the person, of reality, of knowledge, and of value; the aims of education, the nature of the school and the curriculum, the roles and responsibilities of professional educators.
Terms: Fall 2011, Winter 2012
Instructors: Boyd Eric White, Kevin Michael McDonough, Ronald Morris (Fall) Boyd Eric White (Winter)
Restriction: Not open to students who have taken EDER 400.

EDEC 261 Philosophy of Catholic Education (3 credits) *
Overview
Curriculum and Instruction : An exploration of the philosophy of Catholic education, and its relevance in the world today.
Terms: Fall 2011, Winter 2012
Instructors: Charles Ives (Fall) Charles Ives (Winter)
Restriction: Not open to students who have taken EDER 398.
Major Mathematics (54 credits)
Program Prerequisites
Students entering the Major program are normally expected to have completed the courses below or their equivalents. Otherwise they will be required to make up any deficiencies in these courses over and above the 54 credits for the program.

MATH 133 Linear Algebra and Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases; quadratic loci in two and three dimensions.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Shabnam Akhtari, Djivede Kelome, William J Anderson, Adam Clay, Sidney Trudeau (Fall) Djivede Kelome, Wilbur Jonsson (Winter) Nabil Kahouadji (Summer)
3 hours lecture, 1 hour tutorial
Prerequisite: a course in functions
Restriction: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
Restriction Note B: Not open to students who have taken or are taking MATH 123, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.

MATH 140 Calculus 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Stephen W Drury, David Shirokoff, Mark Eric Fels (Fall) Wilbur Jonsson (Winter) Yaiza Canzani Garcia (Summer)
3 hours lecture, 1 hour tutorial
Prerequisite: High School Calculus
Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
Restriction: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
Each Tutorial section is enrolment limited

MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Sungmo Kang (Fall) Antonio Lei, Stephen W Drury, Layan El Hajj (Winter) Hadi Bigdely, Philip Grech (Summer)
Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent
Restriction Note B: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Each Tutorial section is enrolment limited
Required Courses
27 credits
Where appropriate, Honours courses may be substituted for equivalent Major courses.
* Students select either MATH 249 or MATH 316 but not both.

MATH 222 Calculus 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: James G Loveys, Mathew Donald Rogers (Fall) James G Loveys (Winter) Nicolás Fraiman (Summer)

MATH 235 Algebra 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.
Terms: Fall 2011
Instructors: Heekyoung Hahn (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent

MATH 236 Algebra 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. CayleyHamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Terms: Winter 2012
Instructors: Heekyoung Hahn (Winter)
Winter
Prerequisite: MATH 235

MATH 242 Analysis 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Terms: Fall 2011
Instructors: Nikolay Dimitrov, Ivo Klemes (Fall)
Fall
Prerequisite: MATH 141

MATH 243 Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Infinite series; series of functions; power series. The Riemann integral in one variable. A rigorous development of the elementary functions.
Terms: Winter 2012
Instructors: Ivo Klemes (Winter)
Winter
Prerequisite: MATH 242

MATH 249 Honours Complex Variables (3 credits) *
Overview
Mathematics & Statistics (Sci) : Functions of a complex variable; CauchyRiemann equations; Cauchy's theorem and consequences. Taylor and Laurent expansions. Residue calculus; evaluation of real integrals; integral representation of special functions; the complex inversion integral. Conformal mapping; SchwarzChristoffel transformation; Poisson's integral formulas; applications.
Terms: Winter 2012
Instructors: Robert Seiringer (Winter)

MATH 314 Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Wilbur Jonsson (Fall) Ivo Klemes (Winter) Charles Roth (Summer)

MATH 315 Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: JianJun Xu (Fall) JianJun Xu (Winter) Suresh Eswarathasan (Summer)

MATH 316 Complex Variables (3 credits) *
Overview
Mathematics & Statistics (Sci) : Algebra of complex numbers, CauchyRiemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Terms: Fall 2011
Instructors: Heekyoung Hahn (Fall)

MATH 323 Probability (3 credits)
Overview
Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: William J Anderson (Fall) David B Wolfson (Winter) Djivede Kelome (Summer)
Complementary Courses
27 credits selected with the following specifications:
12 credits specifically required of students in the Concurrent B.Sc. and B.Ed. Major Mathematics:

COMP 202 Foundations of Programming (3 credits)
Overview
Computer Science (Sci) : Introduction to programming in a modern highlevel language, modular software design and debugging. Programming concepts are illustrated using a variety of application areas.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Daniel Pomerantz, Jorg Andreas Kienzle (Fall) Daniel Pomerantz, Xue Liu (Winter) Daniel Pomerantz (Summer)
3 hours
Prerequisite: a CEGEP level mathematics course
Restrictions: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computation. COMP 202 cannot be taken for credit with or after COMP 250

MATH 324 Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2011, Winter 2012
Instructors: Russell Steele (Fall) William J Anderson (Winter)
Fall and Winter
Prerequisite: MATH 323 or equivalent
Restriction: Not open to students who have taken or are taking MATH 357
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.

MATH 338 History and Philosophy of Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed in some detail.
Terms: Fall 2011
Instructors: Niky Kamran (Fall)
Fall

MATH 348 Topics in Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : Selected topics  the particular selection may vary from year to year. Topics include: isometries in the plane, symmetry groups of frieze and ornamental patterns, equidecomposibility, nonEuclidean geometry and problems in discrete geometry.
Terms: Summer 2012
Instructors: Benjamin Smith (Summer)
Prerequisite: MATH 133 or equivalent or permission of instructor.
at least 3 credits from:

MATH 317 Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: Fall 2011
Instructors: Peter Bartello (Fall)

MATH 335 Computational Algebra (3 credits)
Overview
Mathematics & Statistics (Sci) : Computational aspects of modern algebra. Computing in groups: algorithms, algorithmic problems in groups, finitely generated abelian groups, free groups and automata, finitely presented groups. Computing in rings: elementary notions of ring theory, ideals of polynomial rings in several variables, Groebner bases, elements of field theory.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.

MATH 340 Discrete Structures 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of mathematical writing, proof techniques, graph theory and counting. Mathematical logic. Graph connectivity, planar graphs and colouring. Probability and graphs. Introductory group theory, isomorphisms and automorphisms of graphs. Enumeration and listing.
Terms: Winter 2012
Instructors: Adrian Roshan Vetta (Winter)
12 credits from:
It is highly recommended that students include MATH 318, MATH 328, MATH 339 and MATH 346 in their complementary courses.

MATH 204 Principles of Statistics 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model.
Terms: Winter 2012
Instructors: Russell Steele (Winter)
Winter
Prerequisite: MATH 203 or equivalent. No calculus prerequisites
Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.

MATH 318 Mathematical Logic (3 credits)
Overview
Mathematics & Statistics (Sci) : Propositional calculus, truthtables, switching circuits, natural deduction, first order predicate calculus, axiomatic theories, set theory.
Terms: Fall 2011
Instructors: James G Loveys (Fall)
Fall
Restriction: Not open to students who are taking or have taken PHIL 210

MATH 319 Introduction to Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Terms: Winter 2012
Instructors: Gantumur Tsogtgerel (Winter)

MATH 320 Differential Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of Euclidean geometry. Local theory of plane and space curves: the Frenet formulas. Local theory of surfaces: the first and second fundamental forms, the shape operator, the mean and Gaussian curvatures, surfaces of revolution with prescribed curvature, ruled and developable surfaces. Geodesic curves on surfaces of revolution. The GaussCodazzi equations, rigidity.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.

MATH 326 Nonlinear Dynamics and Chaos (3 credits)
Overview
Mathematics & Statistics (Sci) : Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Terms: Fall 2011
Instructors: Renato Calleja Castillo (Fall)

MATH 327 Matrix Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.

MATH 328 Computability and Mathematical Linguistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Calculability on an infinite abacus is compared with recursive functions and Turing machines. Categorial, contextfree, generative and transformational grammars are studied for formal and natural languages, with some emphasis on English and French morphology. Machines for generating and recognizing sentences are discussed.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.
 Winter

MATH 329 Theory of Interest (3 credits)
Overview
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2012
Instructors: Neville G F Sancho (Winter)
Winter
Prerequisite: MATH 141

MATH 339 Foundations of Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : A continuation of MATH 338. Topics are chosen mainly from 19th and 20th century mathematics, with some emphasis on philosophical and foundational problems. Sample topics are: progress in number theory, construction of the number system, infinity according to Cantor, logic and foundations from Aristotle to Cohen, Gödel's incompleteness theorem, calculability and programs, formalism versus intuitionism, abstract mathematics and categories.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.

MATH 346 Number Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.

MATH 352 Problem Seminar (1 credit)
Overview
Mathematics & Statistics (Sci) : Seminar in Mathematical Problem Solving. The problems considered will be of the type that occur in the Putnam competition and in other similar mathematical competitions.
Terms: Fall 2011
Instructors: James G Loveys, Sergey Norin (Fall)
Prerequisite: Enrolment in a math related program or permission of the instructor. Requires departmental approval.
Prerequisite: Enrolment in a math related program or permission of the instructor.

MATH 407 Dynamic Programming (3 credits)
Overview
Mathematics & Statistics (Sci) : Sequential decision problems, resource allocation, transportation problems, equipment replacement, integer programming, network analysis, inventory systems, project scheduling, queuing theory calculus of variations, markovian decision processes, stochastic path problems, reliability, discrete and continuous control processes.
Terms: Winter 2012
Instructors: Neville G F Sancho (Winter)

MATH 410 Majors Project (3 credits)
Overview
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Djivede Kelome, Johanna Neslehova, Niky Kamran (Fall) Djivede Kelome (Winter) Djivede Kelome (Summer)
Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
Requires departmental approval.

MATH 417 Mathematical Programming (3 credits)
Overview
Mathematics & Statistics (Sci) : An introductory course in optimization by linear algebra, and calculus methods. Linear programming (convex polyhedra, simplex method, duality, multicriteria problems), integer programming, and some topics in nonlinear programming (convex functions, optimality conditions, numerical methods). Representative applications to various disciplines.
Terms: Fall 2011
Instructors: Yori Zwols (Fall)

MATH 423 Regression and Analysis of Variance (3 credits)
Overview
Mathematics & Statistics (Sci) : Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Terms: Fall 2011
Instructors: Abbas Khalili Mahmoudabadi (Fall)

MATH 430 Mathematical Finance (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing.
Terms: Winter 2012
Instructors: Francois Lamontagne (Winter)

MATH 447 Introduction to Stochastic Processes (3 credits)
Overview
Mathematics & Statistics (Sci) : Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Terms: Winter 2012
Instructors: William J Anderson (Winter)

MATH 523 Generalized Linear Models (4 credits)
Overview
Mathematics & Statistics (Sci) : Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Sliced inverse regression. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. GLIM, S, software.
Terms: Winter 2012
Instructors: David Stephens (Winter)

MATH 525 Sampling Theory and Applications (4 credits)
Overview
Mathematics & Statistics (Sci) : Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Terms: This course is not scheduled for the 20112012 academic year.
Instructors: There are no professors associated with this course for the 20112012 academic year.
In consultation with an adviser, 3 of the 12 credits may be selected from other MATH courses or related disciplines.
Electives (21 credits)
21 credits of electives, of which at least 18 credits must be Science Electives chosen in consultation with the Science Adviser.
The electives must be chosen in such a way that the credit counts needed for graduation are satisfied.