Mathematics @ X!

Whether you are a second year student trying to decide which course to take to complete an "Arts pair", or are planning a schedule of ten courses leading to an Honours Degree in Mathematics, we have designed this booklet for you. It contains information on job opportunities and careers for math graduates, a list of frequently asked questions, descriptions of the various Degree Programs in Mathematics in the Faculty of Science and the Faculty of Arts, and a list of Faculty members and research interests. If you are interested in mathematics and want to learn more, the Department strongly encourages students to contact faculty members to discuss courses, programs, and career opportunities and/or graduate studies in mathematics. A good place to start is the Department Chair, or a professor from whom you have had a course, but don't limit yourself. We'd all like to talk with you about mathematics!

What is Mathematics?

Mathematics is a vast subject. It is the natural language of the physical and life sciences and, increasingly, is becoming a vital tool in business administration and the social sciences. But, in itself mathematics is not a science! (it does not use the scientific method, but rather relies on inductive and deductive reasoning) As a start, one can define mathematics to be the study of structure, and how one can use knowledge of structure in solving problems. Thus, mathematics includes the following:

• Geometry - The study of the structure of curves and surfaces and their properties under various transformations
• Algebra - The study of abstract systems, including the real number system, the integers, and more general structures such as rings and fields.
• Analysis - The study of concepts which require the notions of limits and infinity, including calculus and differential equations. Also called continuous mathematics.
• Discrete mathematics - The study of finite mathematical structures, including combinatorics and graph theory, and the study of computer science algorithms.
• Applied mathematics - This includes the application of all sorts of mathematics to real world problems, and is also known as mathematical modeling.
• Foundations and Logic - Concerns the most fundamental mathematical concepts (such as the notion of a set), and includes traditional symbolic logic as well as new concepts such as fuzzy logic and expert systems which have applications to computer science.
• Mathematics Education - Curriculum development, methods of instruction and assessment in secondary and elementary school mathematics
• Statistics and Probability - Probability theory is the study of processes, which involve in some way the concept of chance… it, has its historical roots in the study of gambling. Statistics concerns the analysis of data from probabilistic processes.

Mathematics at St. F. X.

With the rapid proliferation of the use of computers and information technology, the application of mathematics to different areas has become much easier, and so the use of mathematics has become much more widespread. Thus, the members of the Department believe that a working knowledge of mathematics is an important part of the education of every citizen.

Students in our Mathematics Programs will encounter a range of continuous mathematics, discrete mathematics and statistics, both in the solution of applied problems and in theoretical settings. Several courses in the Program involve projects where students will have the opportunity to synthesize a number of mathematical or statistical ideas and to use appropriate computer tools in completing these projects. Mathematics assists students in examining the logical relations between abstract ideas. More specifically, students should become skilled at recognizing a particular problem as an application of a general theory (thus, reasoning from the general to the specific), and recognizing that there is a common structure in several different problems (thus reasoning from the specific to the general).

1. Understand and be able to communicate the techniques and general directions of the disciplines of mathematics and statistics.
2. Be able to reformulate problems in a mathematical or statistical setting and to understand the nature of the solutions.
3. Be able to study and understand new mathematical or statistical ideas… in particular should be ready to pursue further studies in mathematics or statistics, or in other disciplines closely related to mathematics.

Graduates of the Program have many options. These range from gaining employment in the private sector or in government in a position that requires use of their quantitative and analytical skills, to going on to further study in Graduate School.

How to Get Involved!

1. Come and visit the Department.
   Chair: Martin van Bommel, Annex 24C, 867-3857,
   Administrative Assistant: Rhonda MacDonald, Annex 24A. 867-3972,
   
   

2. Join the Math Society
   Meetings are held in the Departmental Library (Annex 24). Activities include the occasional athletic contest versus the faculty (seems easy!), running the Execoi tutorial service, running a computerized dating service etc. The current co-presidents are:

3. Attend Departmental Seminars
   Held on announced dates in the Departmental Seminar Room, Annex 23A - check for notices.

Frequently Asked Questions

Excellent! Last year, an entire issue of MacLean's magazine was devoted to University education. In a section in which experts offered "hot tips ", the first three pieces of advice given were

1. Definitely stay in school and finish your undergraduate degree.
2. Don't shy away from math, science and computer courses.
3. Don't over specialize. Although a minority of employers and job placement counselors recommend focusing on a specific field, most urge students to remain flexible and to study a wide range of subjects.

The observations made in the MacLean’s article support what we have observed in recent years. Our students graduating with a solid general background in Mathematics, Statistics, and Computer Science have had great success in finding jobs. Although employers may occasionally seek individuals with particular skills, the exact mix of courses isn't as important as how well students have done in those courses.

C) What about Summer Jobs?

Each year, the Department hires a number of students to work for up to four months during the summer. This last summer, ten students (including both math and computer science) were supported on Grants to Department members from NSERC, Human Resources Canada, University Council for Research, and the Educational and Information Technology Committee to work on a very wide range of interesting projects ranging from Web Site Design Using Java, to Database Applications in the Financial Service Sector to Mathematical Modeling in Sports. If you are interested in this type of work, see a member of the Department. In addition to the University Undergraduate Student Research Awards, NSERC has a program of Industrial Undergraduate Research Awards which are tenable at many companies across Canada. You should definitely consider these if you are interested in applied mathematics or statistics. Unlike the University Awards, which are available to students only up to the summer following their third year of University, you may apply for an Industrial Award for the summer following graduation from St.F.X. Another possibility is to apply to Professors in other Departments at St.F.X. who may be looking for someone with good quantitative skills and some computer expertise. You should also check out the Placement Office in Bloomfield for companies in Nova Scotia looking for mathematics or computer science students. For example, Maritime Life visited St.F.X. this Spring seeking summer research, with an interest in statistics, for its head office in Halifax.

D) What are some of the recent Graduates of Mathematics of St. F. X. doing?

Briefly, the answer to this question is that they are doing well in an incredibly diverse number of things. We list below some examples of what some recent Mathematics and Computer Science graduates of the Department of Mathematics, Statistics and Computer Science are doing:

Farzaneh Naghibi '03
Duffy Angevine '03	TBA
Christopher Hawes '03	TBA
Sau Fan Lee '03	TBA
Sai Man Ng '03	TBA
Paul Dion '03	TBA
Beth MacKenzie '03	TBA
Anthony Grover ‘03	TBA
Ryan Lukeman ‘03	Going on to graduate School at Dalhousie
Tommy Rockett ‘02	TBA
Adrian MacKenzie '02	Currently an analyst for Dalhousie Medical School's Population Health Research Unit
Jason Flavin '02	IT manager for the Community Health and Epidemology Department at Dalhousie Medical School
Greg Lee '02	Completed his Masters at University of Alberta, currently working on his PhD
Rene Malenfant '02	TBA
Christain Digout '02	Completed his Masters at University of Alberta, currently working on his PhD
Calvin Thomas '02	Completed his Masters at Dal, currently working for Logic Communications in Bermuda
Cara DeCoste '02	Currently working on B.Ed. at MUN
Elissa MacHattie ‘02	Education
David J. DeCoste ‘02	Completed his B.Ed. at MSVU, currently teaching at a private school in NB
Jenn (Di Persio) Samson ‘02	Employed with Shell Canada
Nick Epifano ‘01	TBA
Kathy Naczk ‘01	TBA
Robert Bradley ‘01	TBA
Sai Yu Ting ‘01	TBA
Jason Samson ‘01	Employed with Shell Canada
Kevin Cry ‘00	Graduate Studies, Software Engineering, University of Calgary
Scott McManus ‘00	Graduate Studies in Theoretical Mathematics at the University of Toronto
Robert Curry ‘00	Completed his Masters at Dal, currently working on his PhD
Kevin Druhan ‘00	Completed his Masters at Dal and is currently is Data Manager for Dalhousie Medical School's Population Health Research Unit
Mark MacIsaac ‘00	Graduate Studies in applied Mathematics at Dalhousie University
David Doyle ‘99	TBA
Shane MacMillian ‘99	Cognos
Sharleen Kalayil ‘99	TBA
Julianne Boucher ‘99	Teaching Mathematics at a High school in Fall River, NS
Blair Fraser ‘99	Game Programmer for Rockstar Games in Vancouver
Paul Schuegraf ‘99	Game Programmer for Rockstar Games in Vancouver
Tim Beck ‘99	TBA
Colleen Meagher ‘99	Currently studying mechanical engineering at Dalhousie
Nicole Di Persio '98	Working for Anderson Consulting
Stephanie Moeller '98	With Statistics Canada in Ottawa
Greg Lukeman '98	Studying Applied Mathematics at Dalhousie
Raylene Delorey '98	Working with DMR in Calgary
Rachel Bland '98	Rachel has accepted an offer from Statistics Canada.
Rod Kelly ‘98	Accepted an offer from DMR Calgary.
Lisa Meager, ‘98.	Lisa has accepted a job offer from Revenue Canada.
Peter Donahue, ‘97	Went on to Computer Engineering at McMaster University
Don Kelly, ‘97	Worked as the UNIX System’s Manager at St.F.X.
Trudy Taylor '97 (Chem/Math)	Attended Medical School at Dalhousie
Ron George '96 (Math/Chem)	Studied Applied Math in Graduate School at UNB, currently In Medical School at Dalhousie
Donna MacKinnon '96	Graduate of the MSc. Program in Applied Statistics at the University of Western Ontario
Chris Boyd '95	M.Sc.(Queens) in Statistics, employed as a biostatistician at Queens University Medical Centre
Marcus Cleary '95	M.Sc.(Queens) in Statistics, employed as an acturary in the U.S.
Tanya Adamsson, ‘95.	Has completed her Master’s program (1998) (funded by NSERC) and then went on to Nortel in Ottawa
Darcy Benoit, ‘95	Received his PhD from Queens and is now an Assistant Professor in the School of Computer Science at Acadia University.
Shawn Allen '95	went on to in Graduate Program in Meteorology at McGill University
Mary C MacAulay ‘94	Secondary teacher at a school on Prince Edward Island.
Pat Furlong, ’94	Is now working with MT&T.
Chris Beck, ‘92	Has completed his Master’s program (1994) and then the Ph.D. program at U. of Toronto (funded by NSERC).

Program Choices

Students interested in Math can pursue either an Honours or Advanced Major Program with a Concentration in either Mathematics or Computational Mathematics. Within Computational Math, one can specialize in one of three possible streams: Numerical Computation, Theorem Proving or Algebraic Structures. Moreover, a student may be in these Programs in either the Faculty of Science or the Faculty of Arts. A quick mathematical calculation shows there are thus sixteen possible Honours and Advanced Major Programs. In addition, one can go for simply a Major in Mathematics in either Faculty, or a Joint Advanced Major or Honours Program which combines Mathematics with either Biology, Physics, Chemistry or Geology ( with Math as either the first or second subject). One can also persue a Math/Economics or Economics/Math major in the Faculty of Arts, or combine business and mathematics in a BBA with a Science Degree. So, a quick calculation gives twenty-nine possible choices!

B) What is the difference between the Advanced Major and Honours Programs.

Apart from the grade requirement listed in the Academic Calendar, the main difference is that the Honours Programs requires more Math/CS courses (ten instead of seven), and the Honours Program specifies that certain upper level courses be taken. Both Programs require the completion of a Senior Thesis. The Thesis requirement for the Honours Program is more rigorous, but, these students receive three course credits for their thesis work.

C) Which Program Do You Recommend?

The question of which Program is for you depends both on your personal interests and career plans. If you really love mathematics go for the Honours Program ...if you are more of a generalist and want to leave room for courses from other Departments, take the Advanced Major Program. Students considering going to Graduate School in either Mathematics, Applied Mathematics or Statistics should take the Honours Program, because successful completion of an undergraduate Honours Program in Mathematics is usually a requirement of admission to most Graduate Programs in these areas.

The Computational Mathematics Program is, in essence, a Program which allows a student to take a combined major in both Mathematics and Computer Science. The core requirements are the same, except that the Computational Program requires a full course in computer programming (CS 160), rather than a half course. The latter part of the Programs differ in that Mathematics students take certain prescribed upper level Mathematics courses, while Computational Mathematics students take a balanced selection of both Mathematics and Computer Science courses. At present, Computational Mathematics students can choose from one of three streams. The streams and their requirements are:

E) What do the Joint Programs in the Faculty of Science Involve?

Joint Advanced Major and Joint Honours Programs are offered by the Department of Mathematics, Statistics and Computer Science in cooperation with the Departments of Biology, Chemistry, Geology and Physics. They allow students who are particularly interested in applying mathematics to one of the sciences great flexibility in putting together a schedule of courses. In these Joint Programs, one of either Science A or Science B must be Mathematics, and the other must be one of the four sciences listed above. If, for example Science A is Mathematics and Science B is Chemistry, the corresponding Program is referred to as Math/Chemistry, while if Science A is Chemistry and Science B is Mathematics, the Program is referred to as Chemistry/Mathematics. The student's advisor, Senior Seminar and Senior Thesis always correspond to the choice of Science A. The course requirements are listed in the Academic Calendar, and include 84 credits of science A and B. and 6 credits of Science C. In addition, each Department has specific courses, which must be included. For example, the requirements for combining Mathematics and Chemistry in an Honours Program are:

• Similar list of required courses may be obtained from the Department Chairs of the appropriate Science Department.
• These Joint Advanced Major and Honours Programs appear to be a good choice if your are considering applying to a professional program such as medicine, dentistry or law. Two of our recent graduates (one in Math/Chem and the other in Chem/Math are currently at Dal Medical School.

This allows a student to pursue an honours program which involves a combined study of two disciplines. At present, one can study Mathematics with Economics as a subsidiary subject or Economics with Mathematics as a subsidiary subject. The Program requires up to 84 credits in the honours and subsidiary subject, with at least 48 credits in the honours subject, and 24 credits in the subsidiary subject. Other requirements are listed in the Academic Calendar. Specific course requirements may be obtained from the Chairs of the Department of Mathematics, Statistics and Computer Science, and the Department of Economics.

Statistics

The minimum course requirements would be an undergraduate degree in Math including the following courses: Introductory statistics - Math 231; probability theory - Math 333; and mathematical statistics - Math 433. It is also recommended that the student take statistical methods - Math 331, and methods of multivariate analysis - Math 435. Some schools also require that the student has taken real analysis - Math 366, although this course can often be completed during the course of the Master’s degree.

There is a very high employment rate for students with a master’s degree in statistics. Although it may be possible to get a job with statistics Canada (see below), or begin actuarial exams (see below), with only an undergraduate degree, there are many other opportunities that would be opened up with a master’s degree.

If you want to apply to Statistics Canada then at the very least you should be near completion of an undergraduate degree in mathematics, and have taken all five statistics courses - Math 231, 331, 333, 433, 435. However, the Statistics Canada exams are quite comprehensive, and a Master’s Degree would considerably increase the chances of a student passing the exam. We note that Statistics Canada also has many openings for individuals who are not statistics specialists. These jobs typically require individuals who have a broad based background which combines mathematics (both pure and applied), statistics and computer science. By getting work experience, coupled, perhaps, with some graduate work at the University of Ottawa or Carleton, these individuals can obtain career advancement while working at Statistics Canada.

Statistics Canada has an annual recruitment of university graduates. The application deadline is in mid-October. More details can be obtained from the employment center.

The starting salary of a statistician is based on his or her university education and experience. Generally speaking, this salary is approximately $30,000 per year. After two or three years’ experience, it usually increases to about $45,000. Various benefits such as a registered pension plan, Dental Care Plan, Health Career Plan, Disability Insurance Plan and Life Insurance are included with employment.

Actuarial Science

Actuaries are professionals trained in mathematics, statistics and economic techniques that allow them to put a financial value on future events. For example, what is the risk that a 16-year-old in the Chicago area will have an auto accident in 1998 and what will the average dollar amount to fix the damage be? How many people aged 40 - 65 will have heart attacks in 2001 and what will their average claim be? How much money does a health insurance company need to set aside to pay for all the claims it will have in a given year? How much should homeowners pay for insurance? Actuaries can answer all those questions and any other risk-based questions by building and running mathematical models.

The skills of an actuary are of great value to insurance companies, investment firms, employee benefits consulting firms, and other types of companies that need to quantify (put a price tag on) financial risks. Typically, it is with this type of firm that actuaries work. Their calculations and projections are the backbone of the insurance and financial security industries. Actuarial work involves lots of math, but actuaries must also be up-to-date on business issues and trends, social science, law, and economics. In other words, actuaries have a well-rounded business approach to problem-solving. And they must be good communicators to explain things to nonactuaries.

Actuarial science is a well-paid profession. At the time of this writing, entry level salaries fall between $32,000 - $45,000. For good candidates, signing bonuses are also common. Top actuaries with many years’ experience often earn over $100,000 a year. Many actuaries eventually leave the technical work behind and move into senior management of companies during the course of their careers. For example, many chief executives of insurance companies are actuaries.

Like doctors, lawyers, or accountants, actuaries must have undergraduate degrees and pass a series of examinations in order to work in the profession. Exam applications are available from the web site http://www.soa.org. The first examination covers multivariable calculus and probability, and covers material taught in Math 267 (Calculus II) and Math 333 (Introductory Probability Theory). Completing at least one of these exams would be an advantage if you are considering applying to a company like Maritime Life for a summer job.

You should aim for a broad-based education that concentrates on business and mathematics, and includes subjects like economics or finance. A double major also might be a plus. Whatever your choice, it's essential to have a strong mathematical background. Your curriculum should include math courses, such as calculus, probability, and statistics. Business courses, such as accounting, management, finance, economics, and computer science, also will increase your career options. Courses in English, speech, and business writing will help you acquire the communications skills actuaries need. And because actuaries are involved in a growing variety of social and political issues, courses in the social sciences and humanities will help round out your capabilities. We note that St. F. X. does not offer special courses in actuarial science, while a few large Universities (notably the University of Waterloo) do offer degrees in actuarial science. Nevertheless, insurance companies often hire students without a degree in actuarial science but with a strong background in mathematics and statistics. Through independent study, coupled with, perhaps, part-time graduate work, these students can obtain career advancement by progressing through the sequence of actuarial examinations.

Mathematics Education

You should take (at least) Math 111/112, Math 201 or 231, Math 253, Math 277, Math 371 and CS 100 or 160. These will give you a basic background in Calculus, Matrix Algebra, Statistics, Discrete Math, Geometry and Computer Science. An examination of the new (1998) Mathematics curriculum for Nova Scotia will show that all of these topics are present in the Grade 10-12 courses, and a good working knowledge of these topics is essential. In addition to these, it is strongly recommended that additional courses should be taken, chosen from Math 333, Math 372, Math 354, Math 347, Math 384, CS 235, Math 366, Math 391, and Math 387.

It is advisable that students include related subjects that feature the applications of Mathematics. For example, Economics 370, Biology 204, Chemistry 231/232, or Physics 241.

The employment market for secondary-level mathematics teachers is quite good now within the province of Nova Scotia, due to the early retirement package, which proved attractive to many teachers in service. Prospects outside the province, particularly in Western Canada continue to be very good. In general, the demand for high school math teachers has been maintained by the fact that the Math Dept. is typically one of the larger Departments in any high school, and the fact that proficiency in mathematics is viewed by the public at large as being of great importance.

Graduate Studies in Mathematics, Applied Mathematics and Statistics

Briefly, there seems to be somewhat more aid available for Graduate Studies than for studies at the Undergraduate level. The best-known financial assistance is funded by NSERC (National Science and Engineering Research Council). These are currently valued at $15,700 per year, and are awarded for graduate studies in any area of the natural sciences or engineering. They are usually tenable at any Canadian University, but a maximum of 50 awards are approved annually for tenure at Universities outside Canada. The selection of nominees is based primarily on academic excellence, research ability or potential, communication skills and leadership ability. Nominees typically are candidates for First Class Honours degrees in a science Department at St. F. X.
In addition to NSERC postgraduate fellowships, many other types of financial aid are available. In fact, nearly all of our graduates who have gone on to graduate school have received some sort of financial aid. This financial aid can be through a direct grant from the University, from an individual Professor's research grant, or from a provincial scholarship, such as offered by the Province of Ontario. These forms of financial aid typically pay on the order of $14,000 per year, and are somewhat easier to get than NSERC Fellowships. The important thing to remember is that Universities do actively seek and recruit graduate students, and that a lot of financial aid is available.

The entrance requirement for most Canadian graduate schools usually states that applicants should hold an Honours degree in mathematics. As an example of a specific University which a significant number of our graduates have attended, the admission requirement for the Department of Mathematics and Statistics at Queen's University states: "Applicants to any of the Master's Programs should have, or expect to have, an Honours degree (or equivalent) with at least upper second class honours standing". As far as specific courses, Math 366 and Math 466 (Analysis I and II) and Math 354 and Math 454 (Modern Algebra I and II) are both strongly recommended for students going on in either mathematics or applied mathematics.
Students going on in statistics or applied statistics should have at least Math 366 and Math 354, together with the statistics courses Math 231 (Statistics for Students in the Sciences), Math 333 (Introductory Probability Theory), and Math 433 (Mathematical Statistics). Ideally, they should also have Math 435 (Methods of Multivariable Analysis). Even with these courses you may not have as many statistics courses as a graduate of a larger University. However, our students have found that their strong background in mathematics (particularly linear algebra and multivariable calculus) has made up for any deficiencies they may have had in statistics.

Honours and Prizes

• Father Ginivan Award: Awarded to the outstanding student in second year mathematics.
• Charlie MacIsaac Award: Given to the outstanding student in statistics in the Department of Mathematics, Statistics and Computer Science.
• A.A. MacDonald: Awarded to the outstanding graduating mathematics student.

Faculty and Research Interests Mathematics

1. Dr. Joe Apaloo Ph.D. (University of Montana)
   • Office location: Annex 22C
   • E-mail address:
   • Area of Interest: Operations Research and Natural Resource Modeling (forestry and fishing)
   • Office Telephone: 867-5274
   • Courses taught 2003-2004: Math 111.14 & 20, 222, Stat 231.21, Math 287
   
   
2. Dr. Wendy MacCaull, PhD (McGill)
   • Office location: Annex 22C
   • Office Telephone: 867-3989
   • E-mail address:
   • Area of Interest: Algebra, logic and approximate reasoning
   • Courses taught 2003-2004: Math 223, Math 277, Stat 201, CS 356, CS 471
   
   
3. Dr. John Quinn, PhD (Wisconsin)
   • Office location: Annex 21 A
   • E-mail address:
   • Area of Interest: Control theory and mathematical modeling
   • Office Telephone: 867-2382
   • Courses taught 2003-2004: Math 111/112, Math 254, Math 205, Math 491/493
   
   
4. Dr. Robert van den Hoogen, PhD (Dalhousie)
   • Office location: Annex 10B
   • Office Telephone: 867-3888
   • E-mail address:
   • Area of Interest: Differential equations and cosmology
   • Courses taught 2003-2004: Math 111/112, Math 221, Math 361, Math 481, Stat 201
   
   
5. Dr. Ping Wang, PhD (Regina)
   • Office location: Annex 22B
   • Office Telephone: 867-2446
   • E-mail address:
   • Area of Interest: Graph Theory
   • Courses taught 2003-2004: Math 111/112, Math 205, CS 335, CS 256
   
   
6. Dr. Ping Zhou (University of Witwatersand)
   • Office Location: Annex 10B
   • Office Telephone: 867-2498
   • Email:
   • Area of Interest: Mathematical Analysis
   • Courses taught: 2003-2004: Math 267 and 372