### Bachelor of Science in Statistics major in Actuarial Science

Degree Codes: Program- BSSTT Plan – BSSTT

This program replaced the B.S. Mathematics (Actuarial Science & Statistics option) in recognition of the fact that actuarial science courses have become statistics-based and at the same time to make it more attractive to prospective students in terms of job opportunities.

#### Objectives and Goals of the BS Statistics Program

The B.S. Statistics program is aimed at producing well-trained graduates with a sound understanding of statistical concepts and their applications. It has a threefold objective:

- To prepare the student for graduate studies in either theoretical or applied statistics, or in other related fields;
- To prepare the student for a teaching career in statistics up to the junior undergraduate level; and
- To prepare the student for immediate work as professional statisticians at the supervisory/managerial level in business, industry, government, engineering and consulting firms, health care organizations, insurance companies, and research institutions.

To fully prepare the student in one or more of these alternatives and to make him/her highly competitive in the job market, a summer practicum is required during the summer period between the 9th and 10th terms of the program. The program also incorporates the use of contemporary statistical software packages to give the student a better perspective on the several applications of statistics.

#### Special Features

The B.S. Statistics program has the following features that make it different from those being offered by the other schools, thus giving graduates of this program an edge over the statistics graduates of other schools:

- It takes only 10 terms (or 3 years and 1 term) to complete the program as compared to the regular 4-year statistics programs of the other schools.
- A summer practicum is required to give the students the opportunity to apply the theories and concepts learned inside the classroom to real-world problems. At the same time, the students are exposed to the workplace environment to help them get employment after graduation.
- This program has a specialization in actuarial science which makes it in effect some kind of a double-degree program in statistics and actuarial science. Hence, graduates of this program could become statisticians and/or actuaries. Furthermore, with enough students and resources in the future, other areas of specialization may be offered such as statistical computing, biostatistics, epidemiology, market research, statistical process control, statistical consulting, etc.
- This statistics program is mathematics-based which gives the students a more solid foundation in terms of the theories in mathematics and statistics. Graduates of this program are expected to be well-prepared for and more capable of pursuing graduate studies in statistics compared to the regular statistics graduates of other schools.
- Students of this program are provided with adequate support in terms of faculty capability; textbooks, journals and references; and computer facilities (hardware and licensed software) at the Mathematics and Statistics Computing Laboratory (MSCL), STRC 316.

LENGTH OF THE PROGRAM – 10 terms and a Summer Practicum

College Algebra (MATH111)

3 units

A course covering the number systems, algebraic functions, relations and graphs, equations, systems of equations, inequalities, and inverse functions.

Trigonometry (MATH112)

3 units

A course including polynomial functions, exponential and logarithmic functions, circular functions, trigonometric identities and equations, complex numbers, law of sines, law of cosines and solution of triangles.

Mathematical Analysis 1 (MATH113)

4 units

A first course in Analysis covering plane analytic geometry, limits and continuity, derivatives of algebraic functions, and their applications.

Prerequisite: College Algebra

Introduction to Statistics 1 (INTSTA1)

3 units

A course covering descriptive statistics, basic rules of probability, discrete probability distributions, normal distribution, sampling distributions, confidence intervals and tests of hypotheses for means, difference of means and variance, t and chi-square distribution and proportion.

Prerequisite: Algebra

Mathematical Analysis 2 (MATH114)

4 units

A continuation of Analysis 1. It covers differentials, indefinite and definite integrals and their applications, derivatives and integrals of logarithmic and exponential functions, trigonometric and inverse trigonometric functions, and techniques of integration.

Prerequisite: Mathematical Analysis 1

Introduction to Statistics 2 (INTSTA2)

3 units

A continuation of Statistics 1. It covers analysis of variance, chi-square tests, regression and correlation analysis and introduction to nonparametric statistical methods.

Prerequisite: Introduction to Statistics 1

Computer for Math 1 (COMMAT1)

3 units

This course covers the fundamentals of logic formulation and their implementation using the Turbo Pascal programming language. Topics discussed in the course includes simple data types, arithmetic operators, built-in functions, assignment operation, IO operation, _oolean expressions, conditional statements, looping structures, compound statements, procedures and functions, parameter passing, arrays and scoping.

Prerequisite: Introduction to Computing and Information Technology for Science Students

Mathematical Analysis 3 (MATH115)

4 units

A continuation of Analysis 2. It covers polar coordinates, indeterminate forms and improper integrals, infinite sequences and series, 3-dimensional space, quadric surfaces, functions of several variables and evaluation of multiple integrals in Cartesian coordinates.

Prerequisite: Mathematical Analysis 2

Introduction to Set Theory (INTOSET)

3 units

A course covering the review of principles of logic, valid arguments and methods of proof; axioms on sets; algebra of sets; relations and functions; the number systems, mathematical induction; countable and uncountable sets; axiom of choice and the continuum hypothesis; ordering and ordinals.

Mathematical Analysis 4 (MATH116)

3 units

A continuation of Analysis 3. It covers vectors in the plane and 3-dimensional space, directional derivatives and gradients, application of partial derivatives to extrema of functions of several variables, evaluation of multiple integrals in spherical and cylindrical coordinates and their applications.

Prerequisite: Mathematical Analysis 3

Matrix Theory (MTRXTHE)

3 units

Concepts in matrix theory with applications to statistics. Matrix operations and properties, special matrices, determinants, eigenvalues and eigenvectors.

Prerequisite: Mathematical Analysis 3

Statistics Packages (STATPAC)

3 units

A course which includes the study of different statistics softwares and packages like PHSTAT, STATISTICA, SPSS, SAS, EVIEWS and others.

Prerequisite: Computer for Math 1

Theory of Interest (THEOINT)

3 units

A course that covers the theory and applications of the measurement of interest, elementary and general annuities, amortization and sinking funds, bonds, and other securities.’

Prerequisite: Mathematical Analysis 3

Statistical Theory 1 (STATHE1)

4 units

A course in probability theory. Topics include, the concept of sample space and events, conditional probability, probability density function, cumulative distribution functions, mathematical expectations, joint and marginal distribution and functions of several random variables. Special distributions such as uniform, binomial, poission, geometric, gamma, beta, exponential, normal distributions, etc., are covered.

Prerequisite: Elementary Statistics, Mathematical Analysis 4, Introduction to Set Theory

Life Contingencies 1 (LIFECO1)

3 units

A course that covers single life functions, the measurement of mortality, life annuities, life insurance, net annual premiums, and net level premium reserves.

Prerequisite: Theory of Interest, Statistical Theory 1

Statistical Theory 2 (STATHE2)

4 units

A course in estimation of parameters and test of hypotheses. Topics include order statistics, limiting distributions, methods of estimation, properties of estimators, hypothesis testing.

Prerequisite: Statistical Theory 1

Sampling Theory (SAMPTHE)

3 units

A course introducing the student to the basic principles of sampling. This course includes the steps to be undertaken in conducting sample surveys, theoretical discussions, on the different sampling designs (simple random sampling, and multi-staged cluster sampling), estimation procedures using the various designs, sample size estimation as well as variance reduction techniques.

Prerequisite: Statistical Theory 2

Linear Models (LINMODE)

4 units

A study of various linear statistical models that arise in practice. Topics include multi-variate normal distribution, distribution of quadratic forms, general linear models, estimation and tests of hypotheses about linear hypotheses, and design matrices giving rise to analysis of variance models.

Prerequisite: Statistical Theory 2, Matrix Theory

Life Contingencies 2 (LIFECO2)

3 units

A course that covers multiple life functions, multiple decrement models, advanced multiple life theory and population theory.

Prerequisite: Life Contingencies 1

Survey Operations (SURVYOP)

3 units

Planning a survey, sampling design, frame construction and tabulation plans, questionnaire design and manual of instruction, data collection and processing, report preparation and presentation.

Prerequisites: Sampling Theory, Statistical Packages

Experimental Design (EXPEDES)

4 units

A study of the various experimental designs in sciences. Topics include the randomized block design, incomplete block designs, analysis of Latin squares, and 2k-factorial experiments.

Prerequisite: Linear Models

Corequisite: Multivariate Analysis

Multivariate Analysis (MULTIVA)

4 units

A course dealing with discriminant analysis, analysis of covariance, multivariate analysis of variances, canonical correlation, factor analysis, cluster analysis, and multidimensional scaling.

Prerequisite: Linear Models

Co-requisite: Experimental Designs Analysis

Survival Models and Graduation (SURGRAD)

4 units

The first part of this course covers topics on Survival Models. It includes estimation of tabular survival models from complete and incomplete data sample study designs using moment and maximum likelihood procedures and estimation of parametric survival models. The second part of this course covers topics on the graduation of life tables. The graduation methods included are Moving-Average; Whittaker, Bayesian, Parametric and Two-Dimensional. It also includes Smooth-Junction interpolation.

Prerequisite: Life Contingencies 1

Time Series and Forecasting (TIMEFOR)

3 units

A course dealing with the different methods of forecasting time series data – classical smoothing procedures and the use of statistical models. The theoretical and model building issues of techniques like exponential smoothing, moving average, seasonal decomposition. ARIMA models, and transfer function economic, agricultural, financial, meteorological among others.

Prerequisite: Introduction to Linear Models

Statistical Quality Control (STATIQC)

3 units

Statistical methods in quality assurance and statistical process control such as control charts, acceptance sampling, response surface methodology and applications.

Prerequisite: Introduction to Statistics 2

Risk Theory (RISKTHE)

3 units

This course covers topics on the economics of insurance; individual risk models for a short term; collective risk models over a single and an extended period and other applications of risk theory.

Prerequisite: Life Contingencies 1

Categorical Data Analysis (CATDATA)

3 units

A course on statistical methods for categorical data. Topics include cross-classification tables, measures of association, logic and loglinear models.

Prerequisite: Linear Models

Nonparametric Statistics (NONPARM)

3 units

A course in distribution-free statistical analysis of data based on ranks. Topics include statistical tests for one-sample problems k-related-sample problems and k-independent-sample problems, and measures of association among variables in non-normal distribution.

Prerequisite: Statistical Theory 2

Actuarial Topics (ACTOPIC)

4 units

A course that covers the estimation of tabular survival models from complete and incomplete data samples study design using moment and maximum likelihood procedures; estimation of parametric survival models, estimation of survival models from general population theory and graduation of life tables.

Prerequisite: Life Contingencies 2

Seminar Course in Mathematics (MATSEMI)

1 unit

A course requiring eight hours of attendance in lectures or seminars conducted by visiting professors or faculty members of the department on various topics and the remaining hours for lectures by the students.

Prerequisite: Junior Standing

Thesis Writing 1 (THSMTH1)

2 units

Introduction to research techniques and research topics. The student is required to submit a thesis proposal.

Prerequisite: Senior Standing

Thesis Writing 2 THSMTH2)

3 units

The course requirement is a bachelor’s thesis done by the student under the guidance of an adviser.

Prerequisite: Thesis Writing 1