** Department
of Mathematics & Statistics**** **03/03

__Chair__**: P.
Keast, Chase Rm.219, keast@mathstat.dal.ca**

__Directors__**: J.Janssen
(Math Majors), Chase Rm.306, janssen@mathstat.dal.ca**

**
Advising times: please arrange an appointment via e-mail.**

** B.Smith
(Stats Majors), Chase Rm.202, bsmith@mathstat.dal.ca**

__Coordinators__**: R.Par?/u> (Honours Math), Chase
Rm.316, pare@mathstat.dal.ca**

** B.Smith
(Honours or COOP Stats), Chase Rm.202, bsmith@mathstat.dal.ca**

** R.J.Wood
(COOP Mathematics), Chase Rm.223, rjwood@mathstat.dal.ca**

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**1st Year** MATH
1000A Calculus I MATH
1010B Calculus II

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**2nd Year** MATH
2001A Intermediate Calculus I MATH
2002B Intermediate Calculus II

MATH 2030A Linear Algebra I MATH 2040B (or MATH 2135) Linear Algebra II

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**3rd Year**

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**4th Year**

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__Degree
Programs__

The Division offers seven programs leading to the BSc. An Honours B.Sc. degree is normally required for any student wishing to do graduate work. For complete information, please see the Dalhousie University Academic Calendar.

**1. The
Honours in Mathematics or Statistics **(4 years - 20 credits) provides a rigorous training in
the discipline.

**2. The
Combined Honours Program **(4
years - 20 credits) is for students who wish to combine two fields of study.

**3. The
Honours Co-op Education Program **(4.5 years) links an Honours degree with industry. Students in
this program

take three work terms.

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**4. The
Advanced Major in Mathematics or Statistics **(4 years - 20 credits) Our standard 20-credit major
degree programs.

**5. The
Advanced Majors Co-op Education Program **(4.5 years) An Advanced Double Major Co-op is also
offered.

**6. The
Advanced Double Major** (4
years - 20 credits) allows a student to specialize in two subjects.

**7. A Concentration in Mathematics or
Statistics **(3 years - 15
credits) furnishes a student with a basic background in mathematics
thereby enabling the pursuit of a variety of interests. Certificate
programs are available for students who wish to
upgrade a 15-credit degree to a 20-credit Advanced Major or Honours degree.

** Certificate
Programs**. Special Certificates are also awarded to
students who complete a certain set of mathematics and statistics courses as
part of a 20-credit degree program.

**1.
Certificate in Actuarial and Financial Mathematics**. This program addresses many of the learning
objectives and

fundamental mathematical and statistical skills required for an actuarial career. It also prepares student for employment in

general financial institutions were modeling, quantitative risk analysis, management of investment instruments, asset and

liability management, life contingencies and insurance assessment, and other complex financial calculations are required.

**2.
Certificate in Applied and Computational Mathematics**. This program is concerned with the
development of the core

mathematical and computational skills required in science, government and industry. Areas of application include everything

from mathematical modeling to operations research to cryptography to software development.

__Career and Advising Information__: Web sites with related links

** **Dalhousie Department of Mathematics &
Statistics, http://www.mathstat.dal.ca

** **Canadian Mathematics Society, http://www.cms.math.ca/Students/en/

Society for Industrial and Applied Mathematics, http://www.siam.org/careers/

American Mathematical Society, http://e-math.ams.org

Mathematical Association of America, __http://www.maa.org/__

*Also visit the Frank G. Lawson Career Information Center at the Student Union Building (see below)

__Additional Academic Advising__

Academic advisors at Student Services can give you general academic advice about defining your educational goals, choosing your major/minor, changing faculties, and help you with academic difficulties. To make an advising appointment telephone 494-3077 or send e-mail to career.portfolio@dal.ca. Where:

Student Services Office, Room G28, Main Level, Killam Library

Telephone: 494-3077

E-Mail: career.portfolio@dal.ca

Website: www.dal.ca/advising

The RegistrarŐs Office provides information and advice on admissions, selection of programs, grade reports and transcripts, letters of permission, academic regulations and appeals, scholarships, bursaries, temporary loans and eligibility for government student financial assistance programs. They may refer you as appropriate to a facility advisor in a department of specific interest. To make an appointment call 494-2450. (Also see Financial Assistance and RegistrarŐs Office). Where

RegistrarŐs Office, Room 133, Arts and Administration Building

Telephone: 494-2450

Website: www.registrar.dal.ca

__Career Counselling and Career
Information Centre__

At Counselling Services, students exploring their academic and career interests will find individual career counselling and group programs on Choosing a Major, What to Do with a Degree in..., Interest Testing, Career Decision Making, Rsum? Writing, Interview Skills, the Hidden Job Market and the Summer Job Search. (Also See Employment and Volunteering)

The Frank G. Lawson Career Information Centre is arranged for easy self-service access to resource materials including the Internet. However, one of our Career Information Assistants will be happy to help you find the information that you need. (Also See Employment and Volunteering, and Study/Work/Volunteer Abroad). Where

Counselling Services

Room 409, Student Union Building

Telephone: 494-2081

Website: www.dal.ca/~cpscic

__Interesting Applications of
Mathematics__: Web sites with related links

** **The Consortium for Mathematics and Its
Application (COMAP), http://comap.com

Mathematical Modeling, http://www-unix.mcs.anl.gov/mathmodeling/

More Mathematical Modeling, http://www.pims.math.ca/education/

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** Courses **(at the 1xxx, 2xxx and 3xxx level).

**NOTE: ** **MATH 1000 and MATH 1010** introduce the
basic ideas of the calculus, and together constitute a solid foundation for
study in the Sciences (Physics, Chemistry, Biology, etc.), as well as for
further study in Mathematics. Students who require one or both of these
classes, but are uncertain of their ability to handle them, are invited to make
use of the diagnostic and remedial services offered in the Mathematics Learning
Centre, located in the basement of the Chase Building. Students are
strongly encouraged to assess their **Precalculus preparation** by trying
the **Diagnostic Test **

Note also that **MATH
1000 X/Y** is offered as a single term class (in both fall and winter terms)
and as a full year class.

**Math
1000: Differential and Integral Calculus I.**

This class offers a self-contained introduction to differential and integral calculus. The topics include: functions, limits, differentiation of polynomial, trigonometric, exponential and logarithmic functions, product, quotient and chain rules, applications of differentiation, antiderivatives and definite integrals, integration by substitution. A sequel to this class is MATH 1010.

**Math
1001: Mathematics for Liberal Arts Students I.**

For students who wish to become acquainted with mathematics as an art rather than as a tool of the sciences. A selection of elementary topics will be discussed with a view to illuminating historical and cultural aspects of the subject. Required work will include a series of written reports on assigned readings and a major essay. This class cannot be used to partially satisfy the BSc mathematics requirement.

FORMAT: Lecture 3 hours, MLC

**Math
1002: Mathematics for Liberal Arts Students II.**

Same as 1001 above, but with a different set of topics. Either one or both of 1001 and 1002 may be taken for credit. This class cannot be used to partially satisfy the BSc mathematics requirement.

FORMAT: Lecture 3 hours, MLC

**Math
1003: The Mathematics of Multimedia.**

This class will introduce students to the mathematics behind animation, graphics and sound. Students will learn how to animate objects at various speeds under linear and nonlinear motion, how to use and manipulate colour under different models, how pitch relates to trigonometric and logarithmic functions, and how curves and matrices can be used to manipulate and compress graphic files. The class will teach students to apply mathematics directly within a programming environment in order to explore the relationship between Mathematics, Computer Science and Art.

NOTE: Registration in this class is restricted to students in the Faculty of Arts and Social Sciences. It cannot be used to partially satisfy the BSc mathematics requirement.

FORMAT: Lecture 3 hours

**Math
1010: Differential and Integral Calculus II.**

A continuation of the study of calculus with topics including: Riemann sums, techniques of integration, elementary differential equations and applications, parametric equations and polar coordinates, sequences and series, Taylor series.

FORMAT: Lecture 3 hours, tutorial 1 hour, MLC

PREREQUISITE: MATH 1000

**Math
1060: Introductory Statistics for Science and Health Sciences.**

See class description for STAT 1060 in the Statistics section of this calendar.

**Math
1110: Finite Mathematics for Commerce.**

This class provides an introduction to the methods of finite mathematics with special emphasis on applications to business. Topics include linear functions, systems of linear equations, matrices, Leontief models, linear programming with emphasis on the simples method, an introduction to probability and Markov chains.

This class may not be used to partially satisfy the BSc mathematics requirement.

FORMAT: Lecture 3 hours, MLC

PREREQUISITE: Nova Scotia Mathematics 442 or equivalent

**Math
1120: Calculus for Commerce.**

This is a elementary calculus class with special emphasis on applications to business. Topics include functions, limits, rates of change, derivatives, one variable optimization and curve sketching, exponential functions, logarithmic functions, functions of several variables, Lagrange multipliers and elementary integration.

This class may not be used to partially satisfy the BSc mathematics requirement.

FORMAT: Lecture 3 hours, MLC

PREREQUISITE: Nova Scotia Mathematics 442 or equivalent

EXCLUSION: MATH 1120 credit cannot be given to those who have already received credit for MATH 1000

**Math
1400: Introduction to Numerical Computing.**

This class introduces students to numerical techniques for solving mathematical problems that they have met in MATH 1000. The students will be introduced to a programming language and a computing environment. Tools to which the students will be introduces will include Matlab and Maple. the topics covered are: introduction to the Unix environment; introduction to C; numerical integration; solving non-linear equations; data fitting and graphing software on Unix stations and on PCŐs; scientific computing libraries; using the Web to obtain solutions to scientific computing problems.

PRE-REQUISITE: MATH 1000

**Math
2001/2002: Intermediate Calculus**

Mathematics 2001/2002 is about calculus in three or more dimensions. It is a direct extension of the single variable calculus studied in first year. Typical problems are (a) physical - find the mass of a solid of varying density, find the steepest path up the mountain-side, (b) geometric - find the equation of a tangent plane or the volume of a solid. Calculus and linear algebra form the core of modern university mathematics. This course is essential not only for students of mathematics but also those of science, particularly physics.

**Math
2030/2040: Linear Algebra**

Mathematics 2030 and 2040 are about various aspects of mathematics that reduce to solving systems of linear equations. Collectively these aspects are called linear algebra. Because the theory of linear algebra is quite elementary, complete proofs are given of most of the theorems. Nonetheless, computational problems play a large role in assignments and tests.

**Mathematics
2051: Problems in Geometry**

A collection of problems that introduce the student to the ideas of combinatorial, projective, inverse, transformational, topological, differential and non-Euclidean geometries.

**Mathematics
2112: Discrete Structures I**

A challenging class, very different from calculus. If you enjoy Mathematics, and especially if you are interested in Computing Science, you will want to give this class your consideration. This class together with MATH 2113.03 offers a survey of those areas in Mathematics which may be classified as dealing with discrete structures. Areas covered include set theory, mathematical induction, number theory, relations, functions, algebraic structures and introductory graph theory. The topics to be discussed are fundamental to most areas of Mathematics and have wide applicability to Computing Science.

**Mathematics
2113: Discrete Structure II**

The class continues CSCI 2112.03/Math 2112.03. It covers some basic concepts in discrete mathematics, which are of particular relevance to students of computer science, engineering, and mathematics. The topics to be covered will include: Solution of recurrence relations, generating functions, modular arithmetic, Chinese remainder theorem, trees and graphs, finite state machines, groups and rings, Boolean algebra.

**Mathematics
2135: Honours Linear Algebra**

In this, the honours version of 2040B, vector spaces and linear transformations are studied. This is a fundamental course for anyone wishing to do advanced work in mathematics or computer science.

**Mathematics
2300: Introduction to Mathematical Modeling and Programming**

This course introduces mathematical modeling and the use of computers for analysis, visualization and exploration in the sciences. Topics range from classical problems of motion to contemporary ones involving simulations, fractals and chaos.

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**Mathematics
2505: Honours Introductory Analysis**

This is the theory of Calculus. Mostly it covers the same topics as in Mathematics 1000 and 1010, i.e. sequences, functions, limits, continuity, differentiability, Riemann integration and series, but from a theoretical point of view. It begins with axioms for the real numbers and proceeds from there in a completely logical development. It is a required class for mathematics Honours students.

**Mathematics
2600: Theory of Interest**

A detailed examination of the theory of simple and compound interest as well as the theory of life contingencies and life insurance premiums. The syllabus includes the material on which exam 2 of the society of Actuaries accreditation examination series is based.

**Math 2790:
Mathematical Problem Solving: Techniques & Methods**

This class will provide an introduction to techniques for solving mathematical problems of the sort encountered in competitions (such as the mathematical olympiad or the William Lowell Putnam competition). This is good course for prospective teachers.

**Mathematics
3030X/Y: Algebra**

Everything about "Modern" algebra you always wanted to know. Learn about groups, rings, and fields. See how new methods can solve 2000-year old problems like circle-squaring and angle-trisecting.

**Mathematics
3070: Theory of Numbers**

Properties of integers and rational numbers are studied in this course. The first half is concerned with divisibility, prime numbers and congruencies, culminating in the deep and important quadratic reciprocity law. Applications of this include properties of sums of squares of integers. The second half of the course includes a thorough discussion of simple continued fractions, and of certain number theoretic functions.

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**Mathematics
3080: Introduction to Complex Variables**

A fascinating subject that combines elegance with important applications in science and engineering. Topics include complex functions, calculus in the complex plane and conformal mapping. This is a useful course for students of Physics and Electrical Engineering.

**Mathematics
3090: Advanced Calculus I**

The course begins with a thorough review of infinite series and power series. The concept of uniform convergence of sequences and series of functions is central to this course. An introduction to Fourier series is given, including is complex form, and more general orthogonal expansions.

**Mathematics
3100: Advanced Calculus II**

This course begins with a study of implicit function theorems, with applications to transformations and multiple integrals. Also covered are improper simple and multiple integrals, functions defined by integrals, and differentiation under the integral sign. Finally, some special topics in differential equations are covered, in particular solutions by infinite series, and Bessel functions.

**Mathematics
3540: Basic Set Theory**

Set theory is the foundation on which modern mathematics is built. This is a good course for prospective teachers and those contemplating work in pure mathematics.

**Mathematics
3110/3120: Differential Equations I & II**

The first course gives a basic introduction to ordinary differential equations with an emphasis on first order and linear second order equations. Various solution techniques including series and Laplace transforms are discussed. The second course gives a basic introduction to the techniques involved in solving linear second order partial differential equations with constant coefficients; in particular the heat, wave and Laplace equations. This includes regular Sturm-Lioville problems and Fourier Series.

**Mathematics
3260: Introduction to Mathematical Modeling Using Differential Equations**

This course is concerned with the formulation and solution of problems in science and technology and is essential for anyone interested in applications.

**Mathematics
3300/3310: Optimization I & II**

An introduction to a topic of fundamental importance to modern business and engineering, including both linear and non-linear programming, the simplex method and numerical algorithms. Math majors and students intending to study Industrial Engineering or Business Administration will find this useful.

**Mathematics
3500X/Y: Intermediate Analysis**

This is a thorough treatment of the basic ideas of analysis - a 'must' for any student with serious ideas about graduate work in mathematics. Topics treated vary somewhat with the instructor but focus on rigorous study of differentiability, continuity and convergence from a more advanced perspective than Math 2505.

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