AS/SC/MATH 1000 3.0 F Differential Calculus (Honours Version)

    2001/2002 Calendar copy: Axioms for real numbers, limits, continuity and differentiability. This course covers slightly fewer topics than AS/SC/AK/MATH 1300 3.0, but covers them in greater depth. It should be taken by all those planning an Honours degree in Mathematics or a Specialized Honours degree in Statistics.
    MATH 1000 aims to develop the students' ability to think and write clearly, logically and precisely, and to read a mathematical text with understanding. One goal is learning how to write proofs. (Of course, we will not spend all our time proving things!)
     It is declared policy of the Mathematics Department to take into account, in the grading of MATH 1000 and MATH 1010, the "newness" to students of such "pure" mathematics courses, in order to encourage interested students to take them. Therefore, although the honours courses are more "theoretical", students who are willing to put a serious effort into them should find it neither easier nor harder to get a high mark (A, B+) in MATH 1000/1010 than to get the same mark in MATH 1300/1310.
     The text will be S.O. Kochman, Calculus: Concepts, Applications and Theory.

Prerequisite: AS/SC/MATH 1515 3.0 or OAC Calculus or equivalent.
Exclusions: AS/SC/MATH 1013 3.0, AS/SC/AK/MATH 1300 3.0, AS/SC/MATH 1505 6.0, AS/MATH 1530 3.0, AS/AK/MATH 1550 6.0, AS/ECON 1530 3.0, AK/MATH 1410 6.0.
Coordinator: TBA

AS/SC/MATH 1010 3.0 W Integral Calculus (Honours Version)

     2001/2002 Calendar copy: Riemann integral, fundamental theorems of calculus, transcendental functions, integration techniques, sequences, series. This course covers fewer topics than AS/SC/AK/MATH 1310 3.0, but covers them in greater depth. It should be taken by all those planning an Honours degree in Mathematics or a Specialized Honours degree in Statistics.
     See MATH 1000 description for remarks on content and grades policy. The textbook will be the same as for MATH 1000.

Prerequisite: MATH 1000 3.0 or permission of the department.
Exclusions: AS/SC/MATH 1014 3.0, AS/SC/AK/MATH 1310 3.0, AS/SC/MATH 1505 6.0, AS/SC/AK/MATH 3110 3.0, AK/MATH 1410 6.0.
Coordinator: TBA

AS/SC/MATH 1013 3.0 FW Applied Calculus I

     2001/2002 Calendar copy: The first half of this course deals with differentiation and the second half with integration. Topics include derivatives of algebraic and transcendental functions, indefinite integrals, techniques of integration, the definite integral and its interpretation as an area.
    Three lecture hours. Tutorials may be offered, and "Mathlab" help will be available. The text will be Varberg, Purcell and Rigdon, Calculus, 8th Ed. If available, secondhand or discounted, 6th or 7th editions of Varberg and Purcell would suffice for most purposes. All students are expected to have a copy of the text.
    Biology and Kinesiology students are advised to consider carefully whether they should be taking MATH 1013/1014 or MATH 1505. Seek advice before enrolling if you are uncertain.
     Applied Mathematics students should, preferably, take the one-credit course MATH1016 during the same term as this course, but in any case must take it within the first 60 credits of their programs.

Prerequisite: AS/SC/MATH 1515 3.0 or OAC Calculus.
Exclusions: AS/SC/MATH 1000 3.0, AS/SC/AK/MATH 1300 3.0, AS/SC/MATH 1505 6.0, AS/MATH 1530 3.0, AS/AK/MATH 1550 6.0, AS/ECON 1530 3.0, AK/MATH 1410 6.0.
Coordinators: Fall: Peter Taylor Winter: TBA

AS/SC/MATH 1014 3.0 W Applied Calculus II

     2001/2002 Calendar copy: Applications of differential and integral calculus (e.g., maxima and minima, areas, volumes of revolution, moments and centroids, etc.), indeterminate forms, improper integrals, Taylor series, simple ordinary differential equations and an introduction to multivariate calculus.
     This course is a sequel to MATH 1013, and will use the same textbook. There are three lecture hours per week.
     Applied Mathematics students should, preferably, take the one-credit course MATH 1017 during the same term as this course, but in any case must take it within the first 60 credits of their programs.

Prerequisites: One of AS/SC/MATH 1000 3.0, AS/SC/MATH 1013 3.0, AS/SC/AK/MATH 1300 3.0, or, for non-Science students only, six credits in the form of: AS/MATH 1530 3.0 and AS/MATH 1540 3.0, or AS/MATH 1550 6.0, or AS/ECON 1530 3.0 and AS/ECON 1540 3.0.
Exclusions: AS/SC/MATH 1010 3.0,AS/SC/AK/MATH 1310 3.0, AS/SC/MATH 1505 6.0,
  AK/MATH 1410 6.0.
Coordinator: 
Kim Maltman

AS/SC/MATH 1016 1.0 F Applied Mathematics Module I

     2001/2002 Calendar copy: Designed for students in Applied Mathematics to complement and enrich the material in AS/SC/MATH 1013 3.0. The module treats the theory in greater depth, and explores extended applications and modelling.
     The focus will be on problem solving. Topics will be related to limits, differentiation, integration, sequences and series. Attendance will be expected.  Evaluation will be based largely on homework assignments and tests.
     Further and updated information on the course will be available at the web site: http://www.math.yorku.ca/~muldoon/

Prerequisite: OAC Calculus or AS/SC/MATH 1515 3.0.
Precorequisite: AS/SC/MATH 1013 3.0. Note: MATH 1016 must be taken
within the first 60 credits of a student's program.
Coordinator:  Martin Muldoon (muldoon@yorku.ca)

AS/SC/MATH 1017 1.0 W Applied Mathematics Module II

     2001/2002 Calendar copy: Designed for students in Applied Mathematics to complement and enrich the material in AS/SC/MATH 1014 3.0. The module treats the theory in greater depth, and explores extended applications and modelling.
    One lecture hour per week. The focus will be on problem solving. Topics will be related to curves, optimization, applications of integration, differential and difference equations.  Attendance will be expected. Evaluation will be based largely on assignments and tests.
     Further and updated information on the course will be available on the web site: http://www.math.yorku.ca/~muldoon/

Prerequisites: AS/SC/MATH 1013 3.0 and MATH 1016 1.0.
Precorequisite: AS/SC/MATH 1014 3.0. Note: MATH 1017 must
be taken within the first 60 credits of a student's program.
Coordinator:  Martin Muldoon (muldoon@yorku.ca)

AS/SC/AK/MATH 1021 3.0 F Linear Algebra I
Formerly AS/SC/MATH 2021 3.0 - before 2001-2002

     2001/2002 Calendar copy: Linear equations, matrices, Gaussian elimination, determinants and vector spaces. This course covers material similar to that in AS/SC/AK/MATH 2221 3.0 but at a more advanced level. Required in Specialized Honours Statistics and all Applied Mathematics, Mathematics, and Mathematics for Commerce programs except the BA Program in Mathematics for Commerce.

Important! Advisors and students: Please see the note on page 12!

     After the concepts in logic and set theory, the most fundamental idea in all of mathematics is that of a FUNCTION. The simplest type of function is a LINEAR function, and linear functions (also called linear transformations) are what linear algebra is about. Thus, linear algebra is mathematically more basic than, for instance, differential calculus, where more complicated functions are approximated locally by linear ones. Apart from underpinning much of mathematics, linear algebra has a vast range of applications - from quantum mechanics (where it is crucial) to computer graphics to business and industry (via statistics and linear programming).
     Additional topics: Euclidean n-space, lines and planes, linear transformations from Rn to Rm , abstract vector spaces, basis and dimension, rank and nullity of a matrix.

Prerequisite:
One OAC mathematics course or equivalent.
Exclusions:
AS/SC/MATH 1025 3.0,
AS/SC/MATH 2021 3.0, AS/SC/AK/MATH 2221 3.0.
Coordinator: 
R.G. Burns

AS/SC/MATH 1025 3.0 FW Applied Linear Algebra

2001/2002 Calendar copy: Topics include spherical and cylindrical coordinates in Euclidean 3-space, general matrix algebra, determinants, vector space concepts for Euclidean n-space (e.g., linear dependence and independence, basis, dimension, linear transformations, etc.), an introduction to eigenvalues and eigenvectors.

Important! Advisors and students: Please see the note on page 12!

The final grade will be based on assignments, term tests and a final exam.  Note (from the Undergraduate Office): MATH 1540 3.0 may not be taken for credit by anyone taking, or anyone who has taken, MATH 1025.

Prerequisite: OAC Algebra and Geometry.
Exclusions:
AS/SC/AK/MATH 1021 3.0,
AS/SC/MATH 2021 3.0, AS/SC/AK/MATH 2221 3.0.
Coordinators:  Fall: Kim Maltman Winter: Buks van Rensburg

AS/SC/AK/MATH 1090 3.0 FW Introduction to Logic for Computer Science

     2001/2002 Calendar copy: The syntax and semantics of propositional and predicate logic. Applications to program specification and verification.  Optional topics include set theory and induction using the formal logical language of the first part of the course.
Note: This course is a program requirement in COSC.
     By taking this course, students will master the syntax and manipulations of propositional and predicate logic, as well their informal semantics.  The proper understanding of propositional logic is fundamental to the most basic levels of computer programming, 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 diverse areas of computer science including digital design, program verification, databases, artificial intelligence, algorithm analysis, and software specification. We will not follow a classical treatment of logic.  Instead we will use an "equational'' treatment. This equational approach will also be the basis for the topics in discrete mathematics treated in MATH 2090.
     See the description of MATH 2090 (later in this minicalendar) for further comment about the importance of formal logic for good programming.
     The text will be Gries and Schneider, A Logical Approach to Discrete Math (Springer).

Prerequisite: One OAC in mathematics or equivalent, or AK/MATH 1710 6.0.
Exclusion:
This course may not be taken for degree
credit by any student who has passed AS/SC/AK/MATH 4290 3.0.
Coordinators: 
Fall: Eli Brettler   Winter: J. Steprans

AS/SC/AK/MATH 1131 3.0 FW Introduction to Statistics I

2001/2002 Calendar copy: Displaying and describing distributions; relations in categorical data; Simpson's paradox and the need for design; experimental design and sampling design; randomization; probability laws and models; central limit theorem; statistical inference including confidence intervals and tests of significance; matched pairs; simulation.
Note: This course is a requirement in the ITEC
program and in Statistics programs.
     Testing a new drug, pricing a derivative asset, evaluating the effects of free trade, making sound investment decisions, and predicting who will win the World Series are all activities that have in common the need to make sense out of ambiguous data. The modern discipline of statistics serves as a guide to scientists, policy makers and business managers who must draw inferences or make decisions on the basis of uncertain information.  
     MATH 1131 provides an introduction to the concepts of statistics with an emphasis on developing an appreciation for variability and a critical attitude towards the use and misuse of statistics in science and business.  Statistical techniques will include confidence intervals for means and tests of significance.
     It is recommended that students have at least one OAC in mathematics, but the mathematical level of the course will be quite elementary. Although students will be making use of the computer to calculate statistics, to create statistical plots, and to obtain a better appreciation of statistical concepts, no previous experience in computing is required.  Students will receive all the necessary instruction about how to use the statistical computer package Minitab.
     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.
     The final grade may be based on assignments and/or quizzes, class tests and a final examination.
The text is
David Moore and George McCabe, Introduction to the Practice of Statistics, 3rd Ed..

Prerequisite: At least one OAC in mathematics is recommended.
Exclusions:
AS/SC/AK/MATH 2560 3.0,
SC/BIOL 2060 3.0, SC/BIOL 3090 3.0, AS/ECON 2500 3.0, AS/SC/GEOG 2420 3.0, AS/SC/KINE 2050 3.0, AS/SC/PHED 2050 3.0, AS/POLS 3300 6.0, AS/SC/PSYC 2020 6.0, AS/SC/PSYC 2021 3.0, AS/SOCI 3030 6.0, AK/MATH 1720 6.0, AK/MATH 2430 6.0, AK/BIOL 3080 6.0, AK/BIOL 3080 3.0, AK/BIOL 3090 3.0, AK/ECON 3470 3.0, AK/PSYC 2510 3.0.
Coordinators: 
Fall: S. Chamberlin     Winter: G. Denzel

AS/SC/AK/MATH 1190 3.0 FW Introduction to Sets and Logic
Formerly: MATH 1120 3.0, MATH 1090 3.0
  
     2001/2002 Calendar copy: Sets, functions, relations, induction, proof techniques, logic and logic circuits, basic combinatorics and some basic graph theory.
Note: This course is a program requirement in
ITEC.
     It is also intended for math majors and other students wanting 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. In recent years this course has been numbered as MATH 1090. Starting in 1999/2000, the (new) course called MATH 1090 ({\it q.v.) is for computer science majors or those intending to be computer science majors, while the traditional topics listed in the calendar copy above now find their home in MATH 1190.
     The textbook is still to be determined.

Prerequisite:  One OAC in mathematics or equivalent, or AK/MATH 1710 6.0.
Exclusions: 
AK/MATH 2441 3.0.
This course may not be taken for degree credit by any student who has passed AS/SC/AK/MATH 1090 3.0 or AS/SC/MATH 1120 3.0 or any 3000- or higher-level MATH course.  Note: Students who plan to major or minor in Computer Science must take AS/SC/AK/MATH 1090 3.0 instead of this course.
Coordinators: 
Fall: TBA    Winter: S.D. Promislow

AS/SC/AK/MATH 1300 3.0 FW Differential Calculus with Applications

     2001/2002 Calendar copy: Limits, derivatives with applications, antiderivatives, fundamental theorem of calculus, beginnings of integral calculus.
Note: This course is required in COSC and ITEC
programs.  Other topics include continuity, the Mean Value Theorem, curve sketching, L'Hospital's Rule and maxima-minima.
     The text will be S.O.\ Kochman, Calculus: Concepts, Applications and Theory, Part I.
     The final grade may be based on assignments, quizzes, class tests and a final examination worth at least 30%.

Prerequisite: AS/SC/MATH 1515 3.0 or AK/MATH 1710 6.0 or OAC Calculus or equivalent.
Exclusions:
AS/SC/MATH 1000 3.0,
AS/SC/MATH 1013 3.0, AS/SC/MATH 1505 6.0, AS/MATH 1530 3.0, AS/AK/MATH 1550 6.0, AS/ECON 1530 3.0, AK/MATH 1410 6.0.
Coordinators: 
Fall: S.O. Kochman.  Winter: TBA

AS/SC/AK/MATH 1310 3.0 FW Integral Calculus with
Applications

     2001/2002 Calendar copy: Transcendental functions, differential equations, techniques of integration, improper integrals, infinite series. Offered in both terms.
Note:
This course is a program requirement in COSC.
     This is the second in a series of introductory calculus courses.  It is designed to follow MATH 1300 3.0.
     Other topics include computation of volume, applications of integration and infinite sequences.
     The text will be S.O. Kochman, Calculus: Concepts, Applications and Theory, Part I or IA as well as Part II.
Note: Some sections, including Section M, will have a computing component. The software Maple will be taught and used to solve certain calculus problems. These sections will have six required Maple assignments.  For further information about these sections, see the Math 1310 Section M course webpage.
     The final grade may be based on assignments, quizzes, class tests and a final examination worth at least 30\%. Some sections, including Section M, will also have graded lab assignments.

Prerequisites: One of AS/SC/MATH 1000 3.0, AS/SC/MATH 1013 3.0, AS/SC/AK/MATH 1300 3.0.  Or, for non-Science students only, six credits: AS/MATH 1530 3.0 and AS/MATH 1540 3.0, or AS/AK/MATH 1550 6.0, or AS/ECON 1530 3.0 and AS/ECON 1540 3.0.
Exclusions:
AS/SC/MATH 1010 3.0, AS/SC/ MATH 1014 3.0,
AS/SC/MATH 1505 6.0, AK/MATH 1410 6.0.
Coordinators:  Fall: TBA   Winter: S. O. Kochman

AS/SC/MATH 1505 6.0 Mathematics for the Life and
Social Sciences

     2001/2002 Calendar copy: A presentation of the elements of single-variable differential and integral calculus, elementary linear algebra and introductory probability and statistics. This course is designed to provide a comprehensive mathematical background for students of the biological and social sciences.  Emphasis is placed on basic mathematical skills and their applications. The text and grading scheme have not been determined yet.

Prerequisite: At least one OAC in mathematics or AS/SC/MATH 1510 6.0.
Exclusions:
AS/SC/MATH 1000 3.0,
AS/SC/MATH 1010 3.0, AS/SC/MATH 1013 3.0, AS/SC/MATH 1014 3.0, AS/SC/AK/MATH 1300 3.0, AS/SC/AK/MATH 1310 3.0, AS/MATH 1530 3.0, AS/MATH 1540 3.0, AS/AK/MATH 1550 6.0, AS/ECON 1530 3.0, AS/ECON 1540 3.0, AK/MATH 1410 6.0.
Coordinator: 
A. Pietrowski

AS/SC/MATH 1510 6.0Fundamentals of Mathematics

     2001/2002 Calendar copy: Designed for the student whose mathematical background is weak and who wishes to take further courses in mathematics. Topics include algebraic equations and inequalities; simple sequences and series; analytic geometry; trigonometry; functions, including algebraic, exponential, logarithmic and trigonometric functions.
     It should be noted that while the acquisition of skills needed for taking (e.g.) a calculus course will be emphasized, an understanding of the underlying concepts will also be required.
     The text will probably be L.I. Holder, A Primer for Calculus (6th Ed.). (This text was used in 1996-2001.)
     The final grade will probably be based on four or five class tests and a final exam.

Exclusions: AS/MATH 1520 6.0, AK/MATH 1710 6.0. May not be taken by any student who has taken or is currently taking another university course in mathematics or statistics, except for AS/SC/MATH 1500 3.0 or AS/SC/MATH 1515 3.0.

Coordinator:  J.M.N.\ Brown

AS/SC/MATH 1515 3.0 FW Introduction to Calculus
Formerly AS/SC/MATH 1500 3.0


     2001/2002 Calendar copy: Elements of differential calculus, anti-derivatives and integrals, with applications. Designed for students who have not taken (or have performed inadequately in) OAC Calculus.
     This course is intended to prepare the above students for courses which have "OAC Calculus or equivalent" as a prerequisite.
     Topics to be discussed include: limits, derivatives, tangents, rate of change, maxima and minima, curve sketching, trigonometric functions, logarithmic and exponential functions, fundamental theorem of calculus, and areas.  
     The text will be Stewart, Davison, and Ferroni, Calculus -- A First Course (McGraw-Hill Ryerson Ltd.).
     The final grade may be based on assignments, quizzes, class tests, and a final examination.

Prerequisite: AS/SC/MATH 1510 6.0 or one OAC course in mathematics.
Exclusion:
AS/SC/MATH 1500 3.0.
  May not be taken by any student who has taken or is currently taking another university course in calculus.
Coordinator:  J. Wick Pelletier

AS/MATH 1530 3.0 FW Introductory Mathematics for Economists I

     2001/2002 Calendar copy: This course introduces and develops topics in differential calculus, integral calculus, and their applications in economics. This course or equivalent is required for all Economics majors or minors; it also satisfies the mathematics requirement for the Schulich School of Business. It is suitable for the Bachelor Program in Mathematics for Commerce, but should not be taken by those who intend to major in any other Mathematics or Statistics program or in Computer Science.  (Same as AS/ECON 1530 3.0.)
     The pair MATH 1530 3.0 and MATH 1540 3.0 is designed to give the student an introduction to mathematics sufficient for a thorough understanding of modern textbooks in economic theory. The emphasis is on the acquisition of tools for later use and on an understanding of both concepts and techniques for applications, rather than on theoretical proofs or a rigorous development of the mathematics involved. The pair is similar to MATH 1550 6.0.
     Topics will include single-variable differentiation, limits, continuity, series, exponential and logarithmic functions, single-variable optimization, and integration. Applications to problems in economics involving supply and demand functions, maximization of profits, elasticity of demand and consumers' surplus will be considered.
     The text last year was Sydsaeter and Hammond, Mathematics for Economic Analysis, together with selected exercises from Haeussler and Paul, Introductory Mathematical Analysis. Both of these texts are published by Prentice Hall.  Last year a "package'' consisting of the first text together with the selected exercises from the second text was available from the York bookstore. It is anticipated that the same texts will be used this year, although students should check with their section instructor at the start of classes.
     The final grade may be based on term tests and/or assignments and a final examination. Instructors will announce details in class.

Prerequisite: AS/SC/MATH 1515 3.0
or OAC Calculus or equivalent.
Corequisite: AS/ECON 1000 3.0 or AS/ECON 1010 3.0.
Exclusions: AS/SC/MATH 1000 3.0, AS/SC/MATH 1013 3.0,
AS/SC/AK/MATH 1300 3.0, AS/SC/MATH 1505 6.0, AS/AK/MATH 1550 6.0, AS/ECON 1530 3.0, AK/MATH 1410 6.0.
Coordinators:  Fall: TBA   Winter: TBA

AS/MATH 1540 3.0 FW Introductory Mathematics for
Economists II

     2001/2002 Calendar copy:This course introduces and develops topics, including matrix algebra, optimization, comparative statics of general function models, and their applications in economics. This course or equivalent is required for all Economics majors or minors; it also satisfies the mathematics requirement for the Schulich School of Business. (Same as AS/ECON 1540 3.0.)
     This course is normally taken by students who have completed MATH 1530 3.0 and are in the Bachelor Mathematics for Commerce Program.
     The material that is covered in the course is mainly matrix algebra and functions of many variables. The material will be covered in a way that will be of interest to students in economics and business. The emphasis will be on the acquisition and use of tools rather than on a rigorous development of the tools. Applications will include the solution of linear equations, and maxima and minima of functions of several variables with and without constraints.
     The text and grading scheme are anticipated to be the same as those for MATH 1530 3.0.

Prerequisite: One of AS/MATH 1530 3.0, AS/SC/MATH 1000 3.0, AS/SC/MATH 1013 3.0, AS/SC/AK/MATH 1300 3.0, AS/ECON 1530 3.0.
Corequisite: AS/ECON 1000 3.0 or AS/ECON 1010 3.0.
Exclusions: AS/SC/MATH 1505 6.0,
AS/AK/MATH 1550 6.0, AS/ECON 1540 3.0. May not be taken by any student who has taken or is taking AS/SC/AK/MATH 1021 3.0, AS/SC/MATH 1025 3.0, AS/SC/MATH 2021 3.0, AS/SC/AK/MATH 2221 3.0, or equivalent.
Coordinators:
Fall: TBA   Winter: TBA

AS/AK/MATH 1550 6.0 Mathematics with Management Applications

     2001/2002 Calendar copy: This course is designed to provide a mathematical background for students in the BBA (Hons.) program. It is also suitable for the Bachelor Program in Mathematics for Commerce, but should not be taken by those who intend to major in any other program in Mathematics or Statistics or in Computer Science.  It includes calculus, matrix algebra and elements of optimization with applications to management. 
     This course is designed primarily for students interested in business
programs. It satisfies a requirement for entry to the BBA (Hons.) program in the Schulich School of Business.
     One theme of the course is optimization -- how to maximize or minimize a function subject to certain constraints. Most of the course is a discussion of calculus and its applications; matrix theory and its applications are also discussed. The emphasis will be on techniques and on applications to business and management problems. The content of this course is very similar to that of the two courses MATH 1530 3.0 and MATH 1540 3.0. These courses will also satisfy the requirements for the programs mentioned above, and they are suitable for those who plan to major in economics.
     Those who wish a stronger foundation in calculus, or who wish to major in any Mathematics program other than those mentioned above, should avoid calculus courses with second digit 5.
     The text will be the latest edition of Haeussler and Paul, Introductory Mathematical Analysis ... (Prentice-Hall). 
     The method for determining the final grade has not yet been decided.


Prerequisite:
AS/SC/MATH 1515 3.0 (may also be taken
as a first-term corequisite) or OAC Calculus or equivalent.
Exclusions:
AS/SC/MATH 1000 3.0,
AS/SC/MATH 1013 3.0, AS/SC/AK/MATH 1300 3.0, AS/SC/MATH 1505 6.0, AS/MATH 1530 3.0, AS/MATH 1540 3.0, AS/ECON 1530 3.0, AS/ECON 1540 3.0, AK/MATH 1410 6.0.  This course may not be taken by any student who has taken or is taking AS/SC/AK/MATH 1021 3.0 or AS/SC/MATH 1025 3.0 or AS/SC/MATH 2021 3.0 or AS/SC/AK/MATH 2221 3.0 or equivalent.
Coordinator: 
P. Olin

AS/SC/MATH 1580 3.0 FThe Nature of Mathematics I

     2001/2002 Calendar copy: Designed to create a positive attitude towards mathematics through an examination of topics relevant to the study of mathematics at the elementary school level. Topics include numeral systems, number theory, nature of algebra and geometry. Intended primarily, but not exclusively, for Education students in the P/J stream.
     The main objectives of this course include providing opportunities for students to achieve success in thinking mathematically and to reflect on the learning and practice of mathematics. The course has been designed with prospective elementary and middle school teachers in mind.  All students who feel that their background in mathematics is incomplete, or whose past experiences have caused them to avoid mathematics, are particularly encouraged to take this course.
     The range of topics is relevant to
the formative and transition years' curriculum. This year there will be a substantial emphasis on mathematics in visual form, including symmetries, patterns and other geometry.  Geometer's Sketchpad (the provincially licensed software) will be used for explorations of geometry in a vivid, visual form. In all work, an exploratory approach will be used, in which students will work in small groups on selected problems and projects, using a mix of hands-on materials, appropriate technology, and pencil and paper. Throughout, the focus will be on developing students' communication skills in written, oral, visual and other forms within groups, with the larger class and the instructor.
     The book Thinking Mathematically, by J. Mason et al., is a basic resource.  Material will also be drawn from other sources, including the internet and recent work on how mathematics is actually done in the human brain. 
     The final grade will be based on a
combination of assignments, projects and a journal. The specific breakdown will be announced after discussion with the class.
     Further information will be available through the web site http://www.math.yorku.ca/Who/Faculty/Whiteley/
Exclusions:
Not open to any student who has taken or is taking another
university mathematics course unless permission of the course coordinator is obtained.
Coordinator: 
Walter Whiteley (whiteley@mathstat.yorku.ca)

AS/MATH 1581 3.0 FW Business Mathematics I

     2001/2002 Calendar copy: This course is an introduction to interest rates (simple, compound), annuities (ordinary, due, deferred), amortization (mortgages, other debts), sinking funds, bonds (face value, bond rate, price, yield rate), and depreciation (straight line, constant percentage).
Note: This course has been designed for the Business and
Society Program (see also below).
    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. While the background required is only (the equivalent of) Ontario Grade 12 mathematics, the course will be a university-level mathematics course that requires problem-solving skills.
     This course will be offered in both Fall term and Winter term, one section per 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. Computers (spreadsheets) will not be used; students will need a hand-held calculator which can at least calculate exponents and logarithms.
     Tentatively, the text will be P. Zima and R. L. Brown, Mathematics of Finance, 5th Ed. (McGraw-Hill Ryerson Limited, 2001), but only about half the text (and not exactly the first half) will be covered. A Solutions Manual for the text will also be available for purchase.
     The grading scheme for the course has not been determined, but it will likely involve one or two tests and a final examination.
     This course is closely related to two other MATH courses. The relationship is: MATH 1581 3.0 plus MATH 2581 3.0 is equivalent to MATH 2580 6.0. So MATH 1581 3.0 contains about half the material that is covered in MATH 2580 6.0 (but not exactly the first half), while MATH 2581 3.0 contains the remaining topics from MATH 2580 6.0. Students who might major in Mathematics for Commerce should take either MATH 2580 6.0 or both MATH 1581 3.0 and MATH 2581 3.0. Either MATH 1581 3.0 or MATH 2580 6.0 will serve to satisfy part of the Core requirements of the Business and Society Program. Spreadsheets are taught in both MATH 2580 6.0 and MATH 2581 3.0.

Prerequisite:  Ontario Grade 12 Mathematics or equivalent.
Exclusion: 
AS/AK/MATH 2580 6.0.
Coordinators: 
Fall: TBA   Winter: TBA

AS/SC/MATH 1590 3.0 W The Nature of Mathematics II

     2001/2002 Calendar copy: A continuation of some of the themes explored in AS/SC/MATH 1580 3.0. Further topics include elements of probability and statistics, the nature of computers, elementary set theory and logic. 
     This course will continue in the spirit of MATH 1580 3.0. The course
will provide additional opportunities for students to develop a positive attitude towards mathematics and to achieve success in thinking mathematically. There will be an emphasis on problem solving both in class and in home-work assignments. Students will be encouraged to reflect on their activities by keeping a journal.
     Many of the projects in the course will be drawn from the book
Thinking Mathematically, by J. Mason, et al. Students should have a copy of this book.
     The final grade will be based on a combination of assignments, projects and participation. The specific breakdown will be announced.

Prerequisite: AS/SC/MATH 1580 3.0 or permission of the course coordinator.
Exclusions:
Not open to any student who has
taken or is taking another university mathematics course (except AS/SC/MATH 1580 3.0), unless permission of the course coordinator is obtained.
Coordinator:
Martin Muldoon (muldoon@yorku.ca)