**MATHEMATICS and STATISTICS**

*Notes on
prerequisites:*

Unless stated otherwise, the minimum grade acceptable in all course prerequisites is a C-. In exceptional cases, course prerequisites may be waived by an instructor. Students will need the instructor’s written permission for waiver of a prerequisite.

If, for any student, more than three calendar years have elapsed since credit was obtained for any course prerequisite, the student concerned should contact the course instructor for further instructions before the course begins. A preliminary assessment test may have to be passed to satisfy the prerequisite.

All students applying for Math courses below the 100-level must write a placement test on dates provided in order to obtain permission to register. For math placement test information refer to the Admissions and Registration section.

The department will
consider exceptional students for advanced standing into certain mathematics courses. See *Advanced
Standing* under Transfer of
Credit section.

Math Centre

UCFV is committed to helping students succeed in their study of mathematics. The Math Centres in Abbotsford and Chilliwack are open at various times throughout the week, Monday to Friday. Students are encouraged to come to the centres for help with math questions. Videos are available for courses below the 100-level; cassette tapes are available for introductory statistics; and computer software, including versions of MAPLE and MINITAB, is available on centre computers for student use. Students may also sign out math books to supplement their course work.

MATH 051:

Fundamental Mathematics *4 credits*

Prerequisites: individual assessment by CCP department.

This is a beginning
mathematics course which provides instruction in whole numbers (addition, subtraction,
multiplication, and division), as well as decimals and fractions.

In some classes, students are assisted by volunteer tutors.

MATH 061:

Fundamental Mathematics *4 credits*

Prerequisites: MATH 051 or individual assessment by CCP department.

This is a basic mathematics course which provides instruction in whole numbers (addition, subtraction, multiplication, and division), as well as decimals, fractions, and percent. Estimation and problem solving are also part of the course.

MATH 071:

Intermediate Business Mathematics* 4 credits*

Prerequisites: MATH 061 or individual assessment by CCP department.

This course consists of a brief review of basic mathematics followed by the metric system, ratio and proportion, percent, statistics, positive and negative numbers, expressions and equations, percentage applications, calculating interest, perimeter, area, Pythagorean rule, and complex word problems.

MATH 072:

Intermediate Algebraic Mathematics *4 credits*

Prerequisites: MATH 061 or individual assessment by CCP department

This course consists of a brief review of basic mathematics followed by the metric system, ratio and proportion, percent, statistics, positive and negative numbers, equations and expressions, algebraic graphing, perimeter, area, volume, Pythagorean rule, and an introduction to trigonometry, polynomials, and scientific notation.

MATH 081:

Advanced Business Mathematics *4 credits*

Prerequisites: MATH 071, Math 10 or individual assessment by CCP department

This course consists of statistics, borrowing money, commercial banking, markup, pricing goods, trade discounts, commission sales, payroll, annuities, banking, and income tax.

MATH 084:

Advanced Developmental Math

(Introductory Math 11 — Algebra) *4 credits*

Prerequisites: MATH 072, UCFV Math assessment (Math Placement Test or CCP assessment)

MATH 084 includes a review of basic operations and signed numbers, variables, equations, polynomials, algebraic fractions, inequalities, factoring, graphing linear equations, radicals, geometry, and trigonometry.

This course is the first half of the math course sequence equivalent to Math 11. It will provide students with sufficient algebra, geometry, and trigonometry to prepare them for MATH 085 and/or some vocational, career, and technical programs. With MATH 085, a standing equivalent to Math 11 (Algebra) will be achieved. On its own, MATH 084 will count as an Advanced Math class for the Advanced Level certificate in CCP.

This course is intended for students who have completed Grade 11 more than three years ago, or who need a refresher course (as determined by a UCFV mathematics assessment), or who have not taken Math 11 (Algebra).

MATH 085:

Advanced Algebraic Math *4 credits*

Prerequisites: MATH 084 with at least a C or Applications of Math 11 with at least a C. All students other than those from MATH 084 must write the Math Placement Test, including students who have successfully completed Math 11 (or Principles of Math 11), or Applications of Math 11.

This course is intended for students who wish to improve and review their math skills. It continues many topics from MATH 084 and introduces functions, quadratic equations, and trigonometry.

This course together with MATH 084 completes the Grade 11 math course. It will enable students to enter Provincial Diploma courses (MATH 094/095).

MATH 094:

Introduction to College Math I *4 credits*

Prerequisites: At least a C in one of the following: Math 11, Principles of Math 11, MATH 085, or Applications of Math 12.

**Note: **All students
including those with Math 11 (or Principles of Math 11) *must* write the MPT, except
those who have passed MATH 085, or Math 12, or Applications of Math 12, with at least a C.

Transferability: none (by itself; see MATH 095)

This course, followed by MATH 095, is recommended for students intending to major in a science, engineering, or technology program who do not have the required Grade 12 prerequisites. Together with MATH 095 it satisfies the provincial level Mathematics 12 requirements and provides the foundations for taking a subsequent calculus course.

Topics include manipulation of algebraic expressions; zeros of quadratic and polynomial functions; equations involving rational exponents, radicals, rational functions and absolute values; inequalities, complex numbers; graphing of these functions; transformations; combinations and composition of simple functions.

MATH 095:

Introduction to College Math II *4 credits*

Prerequisites: MATH 094 with at least a C.

Transferability: OU, (and, with MATH 094, to SFU), UVic

Students using this
course for credit towards a credential must refer to the *Provincial Transfer Guide, *or
check with a program advisor for the amount of credit awarded.

MATH 094 and MATH 095 together complete the Math 12 course. In MATH 095 the students examine logarithmic, exponential, and trigonometric functions, identities, and equations. Additional topics covered as time allows include graphing of rational functions, geometric and arithmetic sequences and series, the binomial series, exponential and logarithmic series, matrices, determinants, vectors, complex numbers, and the complex roots of unity.

MATH 103:

Finite Mathematics *3 credits*

Prerequisites: Math 11 (or Principles of Math 11), or MATH 085 with at least a C

Transferability: SFU, UVic, OU, TWU, and, with MATH 104, to UBC

A collection of useful topics from areas such as set theory, logic, counting theorems, Fibonacci numbers, fractals, combinatorics, and discrete probability.

This course is especially recommended for students of education or social science, but not for students of science or mathematics.

MATH 104:

Introductory Statistics *4 credits*

Prerequisites: A C or better is required in one of the following: Math 11 (or Principles of Math 11), or MATH 085, or Applications of Math 11

Transferability: UBC, SFU, UVic, OU, TWU

An introduction to descriptive statistics, sampling, probability, estimates, hypothesis testing, correlation, and regression.

This course does not involve mathematical proofs of the theory involved (no calculus is required) but does stress an intuitive approach to why and when the procedures can be used.

This course is recommended for arts, education, criminology, and other social science students, or anyone else who wishes to develop the ability to intelligently evaluate published statistical data.

**Note: **Students
with credit for Grade 12 math are expected to take MATH 106. (Transfer students need to
check with the calendar of the receiving institution and the Provincial Transfer Guide)
Students who have credit for or are enrolled in a calculus course are expected to take
MATH 106 or** **MATH 270. Students with credit for MATH 270 are not allowed to take
MATH 104 or l06. Students with credit for MATH 106 are not allowed to take MATH 104.
Students with credit for MATH 104 or 106 may subsequently take MATH 270 in order to
satisfy the requirements for a math minor.

MATH 105:

Math for the Elementary School Teacher *4 credits*

Prerequisites: Math 11 (or Principles of Math 11) with at least a C, or MATH 084/085 with at least a C, or Applications of Math 11 with at least a C+

Transferability: SFU, UVic, OU, TWU, UBC

It has been recognized by various study groups that if a teacher is not at ease with mathematics, those resulting fears and prejudices are communicated to the students. This course is designed to give direct experience of mathematics and to allow you to experience your own thinking ability, thereby restoring confidence in your mathematical ability. We must understand the subject before we can teach it. It should be stressed that MATH 105 is a mathematics course aimed at developing mathematical ability and is not a course in methods of teaching. Topics include properties of real numbers, the basis of arithmetic, other systems of enumeration, plane geometry, functions, probability, and statistics.

MATH 106:

Statistics I *4 credits*

Prerequisites: Principles of Math 12, UCFV MATH 095 with C or better, Applications of Math 12 with C or better, or MATH 109, or MATH 110

Transferability: SFU, UBC, UVic, OU, TWU

An introduction to descriptive statistics, sampling, probability, estimates, hypothesis testing, correlation, regression, and analysis of variance. This course is similar to MATH 104 but involves more probability and inferential statistics. Applications are stressed more than theory but facility with Grade 12 level algebra is expected. No calculus is required.

This course is
intended for commerce and biology students. Anyone without Math 12 or an equivalent must
take MATH 104. Students should check the requirements of their program. MATH 106 is *not
*equivalent to MATH 270, and students cannot expect to obtain credit for both MATH 106
and MATH 270.

Students who have credit for or are enrolled in a calculus course are expected to take MATH 106 or MATH 270.

*See
“Note” for MATH 104.*

MATH 108:

Statistics for Nursing Research *3 credits*

Prerequisites: entry into the Nursing degree program, or Grade 11 Math or equivalent, with C+ or better

The emphasis of this course is on the understanding of nursing research papers. Topics include: types of data and corresponding graphical and summary description; methods of sampling from finite populations; two-way tables and independence; sensitivity and specificity; prevalence and incidence; the normal distribution; regression and correlation; measure of association; sampling proportions and rates; Pearson’s chi-square; hypotheses and confidence intervals; multiple regression, validity and reliability; and experimental versus observational data. Students will use computer software, such as Minitab, or a spreadsheet.

**Note:** It is
not intended to fulfil a statistics requirement for any program other than Nursing.

MATH 109:

Introduction to Mathematical Modeling *4 credits*

Prerequisites: Math 11 or Principles of Math 11 or UCFV MATH 085

Mathematical modeling is an essential tool in a wide variety of disciplines. In this course students learn to represent basic real-world problems in mathematical terms and structures, and analyze the models, and then interpret the results in a meaningful way. Both continuous and discrete models are investigated.

MATH 110:

Pre-Calculus Math *4 credits*

Prerequisites: A recent Principles of Math 12 or UCFV MATH 095, either with at least C-, or Applications of Math 12 with at least a C+, or MATH 109 with a C or higher

Transferability: UBC, SFU, OU, TWU, UVic

This course is required for students who intend to study calculus and who have not obtained a mark of at least B in Math 12 or equivalent.

MATH 110 is intended to help to strengthen students’ basic algebraic skills, to re-examine functions including rational, exponential, logarithmic, trigonometrical and inverse functions, and to provide a general introduction to the notions of calculus, namely, differentiation and integration.

**Note: **Credit
cannot be obtained for both MATH 094/095 and MATH 110.

MATH 111:

Calculus I *4 credits*

Prerequisites: Principles of Math 12 with B or higher, or UCFV MATH 094/095 with B average or higher, or MATH 110 with C+ or higher

Transferability: UBC, SFU, UVic, OU, TWU

The study of calculus represents a major step in your education. Mathematics, previous to this subject, dealt with the description of static and non-changing phenomena. During the latter part of the 17th century, Isaac Newton developed a mathematical description which dealt with changing phenomena. This mathematics of change is now called differential calculus.

Calculus I is offered to students who wish to develop their mathematical ability further. This course is a requirement for most first-year science programs. Topics include limits, derivatives, applications of derivatives such as optimization and related rates, antidifferentiation, definite integrals and the fundamental theorem of calculus.

**Note:** Credit
cannot be obtained for more than one of MATH 111, MATH 113, or MATH 115.

MATH 112:

Calculus II *4 credits*

Prerequisites: MATH 111 with C or better

Transferability: UBC, SFU, UVic, OU, TWU

Calculus I was concerned with the determination of the characteristics of change of a given quantity. In Calculus II, the change is examined in the opposite manner: if we know the changing characteristics of a quantity, can we determine what that quantity is?

Topics will include: Techniques of integration, application of the definite integral to various problems such as areas, volumes and surfaces of revolution, improper integrals, indeterminate forms, polynomial approximations, sequences and series.

**Note: **Credit
cannot be obtained for more than one of MATH 112, MATH 114, or MATH 116.* *

MATH 115:

Differential and Integral Calculus I *4 credits*

Prerequisites: Principles of Math 12 with C+ or higher, or UCFV MATH 094/095 with C+ or higher, or UCFV MATH 109 with B or higher, or UCFV MATH 110 with C+ or higher, or a C+ in Applications of Math 12

Transferability: UBC, SFU, TWU, OU, UVic

This calculus stream (MATH 115/116) is recommended for students of Business Administration and Computer Information Systems. (Please see transfer guide for transferability to other universities.) This course is based on modelling real data with piecewise continuous models. The current and future behaviour of the model is analyzed using the techniques of differential calculus of one variable, including optimization and curvature analysis, and the results are interpreted in real-life terms. Also included in the course are integral calculus of one variable topics: finding the total accumulation of change, Riemann Sums, the Fundamental Theorem, finding anti-derivatives, applications involving measuring the effects of change, and very simple differential equations.

**Note:** This
course will be first offered in 1999/2000.

**Note: **Credit
cannot be obtained for more than one of MATH 111, MATH 113, or MATH 115.

MATH 116:

Calculus II for Business and CIS *4 credits*

Prerequisites: MATH 113 or 115 with C or better

Transferability: UBC, SFU, TWU, OU, UVic

This calculus stream is recommended for students of Business Administration and Computer Information Systems. (Please see transfer guide for transferability to other universities.) This course continues from MATH 115 and relies heavily on modelling from real data. The topics include: multivariate differential calculus, differential equations, matrices, solution of simultaneous linear equations and simultaneous differential equations.

**Note:** This
course will be first offered in 1999/2000.

**Note:**Credit
cannot be obtained for more than one of MATH 112, MATH 114, or MATH 116.

MATH 125:

Introduction to Discrete Mathematics *4 credits*

Prerequisites: C average or better in Math 094/095, or a B or better in Math 105, C or better in Principles of Math 12, or Applications of Math 12 with at least B

Transferability: OU, SFU, UVic

Discrete math is a new and important part of mathematics, and is concerned primarily with the analysis and computational representation of ‘finite structures’. Its applications are widespread in modern technology and include scheduling, network construction, data communications, and computer engineering. This course serves as an introduction to some of the basic techniques of the discipline, including methods of counting, modular arithmetic, and formal logic. The focus of the course will be on formulating problems into mathematical models, and on methods applicable to the analysis of these models.

**Note:** Credit
cannot be obtained for both MATH 125 and MATH 243.

MATH 152:

Linear Algebra for Engineering *4 credits*

Pre- or Corequisite: MATH 112

Transferability: UBC, OU, UVic, UNBC

This course is designed for students seeking a career in engineering. It covers the solutions of linear systems of equations, vector spaces, linear dependence and independence, matrix algebra, determinants, orthogonal transformations and bases, eigenvalues, diagonalization, symmetric matrices, the algebra of complex numbers, and linear systems of differential equations.

**Note**: Credit
cannot be obtained for both MATH 152 and ENGR 152.

MATH 211:

Calculus III *3 credits*

Prerequisites: MATH 112 with C or better, or MATH 114 with B+ or better; or MATH 116 with C or better

Transferability: UBC, SFU, UVic, OU, TWU

The concepts of first-year calculus are extended to cover more general cases. The generalization enables you to attack a much larger class of problems.

In particular, the calculus of one variable is extended to cover the calculus of many variables.

Topics include solid and analytic geometry, partial derivatives and applications, multiple integrals.

MATH 212:

Calculus IV *3 credits*

Prerequisites: MATH 211 with C or better

Transferability: UBC, SFU, UVic, OU, TWU

The topics of this course are the basic results of vector calculus. They include review of multiple integrals and jacobians, integration in vector fields, line integrals, work, circulation, flux, Green’s theorem in a plane, surface area and surface integrals, the del notation, the divergence theorem, Stokes’ theorem, conservative fields, and exact differential forms (as time permits).

This is a fundamental course for students of physics and engineering.

MATH 214:

Analysis *3 credits*

Prerequisites: MATH 112 with at least a C (B recommended)

Transferability: UBC, SFU, UVic, OU, TWU

This course provides a first contact with a more analytic approach to many of the themes used in calculus. Topics include induction, limits of sequences and functions, and continuous and differentiable functions.

MATH 221:

Linear Algebra *3 credits*

Prerequisites: MATH 112 with a C or better; or MATH 116 with C+ or better

Transferability: UBC, SFU, UVic, OU, TWU

This course in linear algebra offers an introduction to the strength and flexibility of mathematics. Powerful general results are derived, and can then be applied to specific problems in areas such as physics, engineering, commerce, or chemistry. At other times, the process is reversed and particular problems are used to motivate far-reaching results. Topics include linear systems, matrix algebra, vector spaces, linear transformations and diagonalization.

MATH 225:

Topics in Discrete Mathematics *3 credits*

Prerequisites: MATH 125

Transferability: SFU, OU, UVic

This course introduces the student to some of the most useful types of ‘combinatorial structures’, for example, graphs, trees and recurrence relations, all of which play an important role in the mathematics of computers and computation. Topics include recurrence relations, asymptotics, graphs and digraphs, trees, and applications.

**Note:** Credit
cannot be obtained for both MATH 225 and MATH 243.

MATH 235:

Mathematical Modeling *3 credits*

Prerequisites: MATH 112 or MATH 116

Corequisites: At least one course from MATH 106, 152, 211, 221, or 270

Transferability: UBC, SFU, UVic, TWU

This course
introduces the student to the techniques of *mathematical modeling*: the construction
of a mathematical description of a real-world situation, and the analysis of this
description. All computation will be done in a CAS (computer algebra system) environment
(such as MAPLE), enabling the student to concentrate on creating and criticizing the
models.

MATH 255 (formerly MATH 310):

Ordinary Differential Equations *3 credits*

Prerequisites: MATH 112; OR MATH 114 with at least a C+; MATH 152 unless currently enrolled in MATH 221 OR PHYS 221

Corequisites: MATH 211; MATH 221 or PHYS 221 unless MATH 152 already completed.

Transferability: UBC, SFU, UVic

Most mathematical models of a system, whether from engineering, biology, physics, sociology, geography, psychology or economics, are in the form of differential equations.

This course examines some methods of solving certain types of differential equations. Applications are stressed. Topics include first- and second-order linear differential equations, linear systems, non-linear equations, series solutions, and Laplace transform methods.

**Note: **Credit
cannot be obtained for more than one of MATH 310, 255 or ENGR 255.** **

MATH 270:

Introduction to Probability and Statistics *4 credits*

Prerequisites: MATH 112, or MATH 114 or MATH 116 with C or better

Transferability: UBC, SFU, UVic

An introduction to probability and statistics using calculus, for engineering, science and mathematics students.

*See
“Note” for MATH 104.*

MATH 280:

Further Topics in Probability and Statistics *3 credits*

Prerequisites: MATH 270

Transferability: SFU, UBC, OU

Topics include conditional probability and expectation, Markov chains, Poisson processes, lifetime distributions and reliability, general inference techniques, fitting and testing simple probability models, application to production management and quality control, sequential analysis (as time permits).

MATH 302:

Analysis of Observational

and Experimental Data *3 credits*

Prerequisites: MATH 104 with at
least a B+, **or** MATH 106, **or** MATH 270

Transferability: UVic, SFU

A practical course on the use and understanding of linear models, based on a major statistical software package. The emphasis throughout is on the construction and interpretation of simple linear models used to represent observational points fairly near the overall mean; and on understanding which model represents the alternate hypothesis and what restriction of this model represents the null hypothesis.

MATH 308:

Linear Programming *3 credits*

Prerequisites: MATH 221 or MATH 114, with at least C+ recommended.

Transferability: OU, SFU

An introduction to the theory and applications of linear programming. Topics include the geometry of linear programs, duality, the simplex method, networks, and the application of duality.

MATH 316:

Numerical Analysis *3 credits*

Prerequisites : MATH 112 or 114, MATH 221, and knowledge of a programming language acceptable to the department.

Transferability: SFU

Discussion, construction and application of numerical computing solutions to mathematical problems, including linear algebra, differentiation and integration, non-linear equations, the approximation of functions and ordinary differential equations

MATH 320:

Advanced Calculus of One Variable *3 credits*

Prerequisites: MATH 214

An introduction to some techniques of real analysis. Topics include infinite series, uniform convergence, Taylor series, improper integrals, and Fourier series.

MATH 322:

Complex Variables *3 credits*

Prerequisites: MATH 211

Transferability: OU, SFU

An introduction to complex analysis, and its applications.

MATH 330:

Design of Experiments *3 credits*

Prerequisites: MATH 302

Transferability: SFU

The construction and
analysis of standard experimental designs. Topics include: linearity, randomization,
blocking, use of covariates, the 2^{k} factorial design, Daniels’ normal
plotting, fractional factorials, replications, response-surfaces, variance components,
cross-over designs, split-plot design, error-in-measurement problems and attenuation.

Emphasis will be on the conduct, assumptions, implications and rationale of particular designs. Students will be expected to use suitable software, e.g. MINITAB, when necessary. Students will be expected to design, conduct, analyze and report an experiment illustrating at least one of the major designs discussed.

MATH 343:

Applied Discrete Mathematics *3 credits*

Prerequisites: MATH 243 or MATH 225 and knowledge of a computing language acceptable to the instructor

An introduction to discrete modelling, generation of combinatorial objects, applications to scheduling, and application to graphs.

MATH 350:

Survey Sampling *3 credits*

Prerequisites: MATH 106 with at least a B, or MATH 270

An introduction to the theory and practice of survey sampling.

MATH 360:

Operations Research I *3 credits*

Prerequisites: MATH 211, MATH 221

Overview and extensions of linear programming; transportation, assignment, network algorithm; dynamic programming; integer programming; nonlinear programming; optimization with constraints; separable programming; the minimum cost flow problem; PERT and CPM.

MATH 381:

Mathematical Methods I *3 credits*

Prerequisites: MATH 211, 212, 310, 221. PHYS 111/112 recommended

This course covers a wide range of mathematical techniques: calculus problem-solving devices; Fourier series, Fourier integrals; the gamma, beta, and error functions; Bessel functions, Legendre, Hermite and Laguerre polynomials, Sturm-Liouville systems; partial differential equations; and calculus of variations.

**Note: **Credit
cannot be obtained for more than one of MATH 381, PHYS 381, or ENGR 257.

MATH 390:

Time Series and Forecasting *3 credits*

Prerequisites: MATH 270, 302

An introduction to the basic ideas of time-series analysis and to the Box-Jenkins ARIMA family of models in particular. The emphasis of the course is on practical implementation of the methods.

MATH 402: Generalized Linear
Models

and Survival Analysis *3 credits*

Prerequisites: MATH 270, 302

This course applies the methods of linear model analysis, developed in MATH 302, to non-normal data.

MATH 420:

Empirical and Non-parametric Statistics *3 credits*

Prerequisites: MATH 211, 270. MATH 221, and additional upper-level statistics courses recommended.

Empirical and non-parametric statistics are used either when little can be assumed about the underlying distribution or when it is very complex. These methods are based on order statistics, rankings, or resampling, and are very useful when a relatively quick answer is required.

MATH 438:

Advanced Linear Algebra* 3 credits*

Prerequisites: MATH 221 and at least two upper-level Math courses

Techniques and applications of linear algebra. Vector spaces; linear functionals; the singular value decomposition; the generalized inverse; canonical forms; the spectral decomposition.

MATH 439:

Modern Algebra *3 credits*

Prerequisites: MATH 221

Transferability: SFU

This course is an introduction to the ideas of modern algebra with emphasis on group theory.

MATH 445:

Introduction to Graph Theory *3 credits*

Prerequisites: MATH 225

An introduction to graph theory and its applications.

MATH 450:

Statistical Distribution Theory *3 credits*

Prerequisites: MATH 211, 221, 270, and at least two upper-level Math courses.

This course provides the mathematical theory underlying statistical inference.

MATH 451:

Parametric Statistical Inference *3 credits*

Prerequisites: MATH 450, or MATH 270 and (MATH 280 or MATH 460) and MATH 211 and at least two upper-level courses.

A course on the ideas and techniques of the main schools of parametric statistical inference.

MATH 460:

Operations Research II *3 credits*

Prerequisites: MATH 270, MATH 360

Topics include decisions under uncertainty, decision trees, utility, Bayesian analysis; renewal theory, stochastic inventory control, machine maintenance problems; Markov chains, Chapman-Kolmogorov equations; queuing models; multiserver queues, network of queues, applications of queuing models; Markov decision processes, applications to inventory control and scheduling problems; simulations, random variables, reduction of variance, number of runs; reliability theory, systems with repair.

MATH 470 :

Methods of Multivariate Statistics *3 credits*

Prerequisites: MATH 211, 221, 270, 302, and two additional upper-level courses

The course is an
extension of the linear model methods of

MATH 302 to the multivariate situation. It examines a range of widely-used multivariate
statistical techniques, their relationship with familiar univariate methods, and the
solution to practical problems.

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