Department of Mathematics and Statistics

BACHELOR (LICENSE)

MATHEMATICS (B.SC.)

Goal

If BA covers all areas of mathematics. At the heart of your training, the subjects addressed – algebra to the computer through the analysis, geometry, discrete mathematics, numerical mathematics as well as probability and statistics – will give you a base strong and extended mathematics.

You can also deepen pure mathematics, applied mathematics and statistics or begin studying a scope as actuarial science, economics, computer science, physics and education.

Ability

Love learning and analyze concepts. Love symbols and abstractions. A passion for problem solving. Loving disseminate, transmit information and teach. Owning an analytical and logical mind. Control operations and mathematical abstractions. Be resourceful, persistent and thorough. Being versatile and have communication skills and teamwork.

Opportunity

You may like to refer you to the field of research, both public and private, and work in any areas of pure and applied sciences. Major computer companies could, too, will benefit from your skills.

Under certain conditions, you can legally qualify for secondary education by obtaining 61 credits mainly related to internships and teaching in the Bachelor of Secondary Education – Mathematics.

Professions

Teacher

Mathematician

Statistician

Employers

Research centers

IT companies

Educational Institutions

Governments

CONTINUATION OF STUDIES FOR GRADUATE

This leads to bachelor graduate studies, including pure or applied mathematics, statistics, computer science, economics, administration, teaching and engineering

CONDITIONS OF ADMISSION

All requirements must be met when undertaking the program.

The applicant must meet the following requirements:

Be 18 years or older.

Hold a high school diploma (Bac II) or its equivalent.

Having left school early.

Applicants presenting a combination of education and relevant experience deemed equivalent to that required of the holder applicant may be eligible as a result of the analysis of the file.

The program is limited enrollment, the number of places is very limited.

Selection criteria

The application is analyzed on the basis of the quality of academic record.

Laptop

In undertaking its program, the student must acquire, from the first session, a portable computer equipped with a number of software, allowing the applicant to undertake the course of his research. Proficiency in basic computer functions and common software is essential. Introductory courses to specialized software are offered outside the program.

Knowledge of French

The student admitted to the mathematics department must comply with the provisions relating to the application of the Policy on the use of French at the University GOC

Non-francophone candidate

The candidate whose language of instruction in primary and secondary education is not the French must demonstrate a minimum level of knowledge of the French language. His skills in written French will be assessed on arrival and, where applicable, a patch French courses could be added to its journey.

 

PROGRAM STRUCTURE

GRADE

Bachelor (Licence) in Mathematics (BSc.)

*This page presents the official version of the program. The University G.O.C. reserves the right to change the content without notice.

EHE – studies off-campus

EHE1MAT Studies – International profile – Bachelor’s degree in Mathematics

TRACKING PROGRAM(96 credits)

MATHEMATICS (88 CREDITS)

The student can take three optional practical training courses: MAT-2590-MAT 2591 and MAT-2592. The credits of these courses are in addition to the credit requirements of the program. To register, contact the program director.

IFT-1004: Introduction to Programming (3 credits)

Description

Paradigms and programming languages. Introduction to problem solving with Python. The interpreted language, Python, to a compiled, structured language, the C language specification of a problem and functional decomposition. Modular programming. Notions of black box, interface, precondition and postcondition. Error handling and exceptions management mechanism. Recursion. Introduction to complexity of algorithms. Programming standards.

MAT-1110: Calculation of functions of several variables (3 credits)

Description

Differential calculus of functions of several variables: composite functions; directional derivative; Taylor formula; implicit function theorem; extrema. Double and triple integrals: Fubini theorem; change variables; coordinate systems; improper integrals. Complex numbers: representations; polynomials; series; exp functions z, sin z and cos z.

MAT-1200: Introduction to Linear Algebra (3 credits)

Description

Systems of linear equations, matrix formulation, step shape, existence and uniqueness of solutions, inverse, Gauss-Jordan, factoring, decisive. Introduction to vector spaces: linear independence, basis, dimension, subspace, applications systems, scalar product, projection. Linear Transformations: kernel, image, change of basis, rank theorem, symmetric matrices, orthogonal, positive definite, geometric appearance. Orthogonality, least squares method. Own values and vectors: diagonalization, geometric interpretation, applications.

MAT-1300: Elements of Mathematics (3 credits)

Description

Logic: logical equivalence, quantifiers, proof techniques, mathematical induction principle. Sets: basic operations, indexed families, Cartesian product, order relations and equivalence. Functions: injectivity, surjectivity, bijectivity, image, inverse image, composition, invertibility. Integers: arithmetic, divisibility, congruence modulo N. polynomials: arithmetic, divisibility, irreducibility, roots. Introduction to algebraic structures: rings and body.

MAT-1500: Geometry (3 credits)

Description

Points and straight outstanding of the triangle inscribed circles, exinscrits circumscribed right and Euler circle; oriented angles; arc capable of Apollonius circle, power, beam, Classic Construction iron; divisions and harmonic beams, polar; regular polygons; isometries and similarities.

MAT-1100: Analysis I (3 credits)

Description

Real numbers: inequality, supremum, infimum. Rational and irrational; countable sets. Suites limits. Suites defined by induction. Bolzano-Weierstrass Theorem. Cauchy sequences. Series: convergence. Classical criteria for positive series. Cauchy criterion, absolute convergence, alternating series. Power series. Functions of a real variable. Continuity. Achievement of terminals and the intermediate value theorem.

MAT-1310: Discrete Mathematics (3 credits)

Description

This course covers the following topics of discrete mathematics: counting principles and combinatorics; graph theory and trees; generating functions; introduction to formal languages. Themes underlying these main themes are also addressed: proof by induction, suites defined by induction, order and preorder are examples.

MAT 2110: Differential equations and vector calculus (3 credits)

Description

Linear differential equations. Vector fields. Geometry of curves and surfaces. Line and surface integrals of scalar and vector fields. Fundamental theorem of calculus for vector fields. Potential fields. Fundamental theorems of vector calculus.

MAT-2200: Advanced Linear Algebra (3 credits)

Description

Vector spaces. Subspaces, direct sums, bases. Linear applications, the rank theorem, trace, values and clean spaces. Diagonalization, Jordan Curve Theorem. Euclidean spaces: scalar product, dual and assistant, orthogonal, symmetric and normal operators, Gram-Schmidt process and QR factorization. Matrix standards. Hermitian spaces: normal, unitary operators, spectral theorem. Quadratic forms. Applications.

STT-1500: Probabilities (3 credits)

Description

Axioms of probability theory. Conditional probability and independence. Discrete random variable and random variable absolutely continuous. Random vector. Distribution function. Transformations of random variables. Moments of a random variable. Generating function. Convergence: in probability, almost sure and law. Limit theorems in an elementary form.

MAT-2100: Analysis II (3 credits)

Description

Definition of the derivative. Theorems of Rolle and mean value, rule Hospital. Taylor’s theorem. The Riemann integral. Fundamental theorem of calculus. Improper integrals. Uniform convergence of sequences and series of functions. Transcendental functions. Definition and properties of functions exp x, log x, sin x.

MAT-2300: Algebra I (3 credits)

Description

Groups subgroups, Lagrange theorem, homomorphisms, normal subgroups, quotient groups, isomorphism theorems, lattice theorem, Cartesian products, theorem of finite abelian groups, Cauchy, and action of a group of formula orbit-stabilizer. Rings: homomorphisms, rings, ideals, quotient rings, invertible elements, zero divisors and body.

MAT-2400: Numerical Methods (3 credits)

Description

Numerical computation. Iterative methods. Approximation. Integration. Trigonometric approximation.

STT-4000: Mathematical Statistics (3 credits)

Description

Reminder of probabilities law of large numbers and central limit theorem. Random sample, statistics and sample distribution. Chi-square law, the Student and Fisher’s. Estimator, bias, MSE, efficiency, Cramer-Rao. Maximum Likelihood. Confidence interval. Hypothesis testing, Neyman-Pearson lemma, uniformly most powerful test, likelihood ratio test.

MAT-3100: Analysis III (3 credits)

Description

Metric spaces: definition, examples, completeness. Topology. Continuous applications: preserving the compactness and connectedness. Principle of contraction. Functions of several variables: the derivative as a linear transformation. Local inversion theorem and implicit function theorem, Lagrange multipliers.

MAT-3110: Differential Equations (3 credits)

Description

Linear equations. Laplace Transformation. Linear systems of differential equations. Introduction to the qualitative theory. Boundary value problems and introduction to partial differential equations. Fourier series. Separation of variables for partial differential equations.

MAT-3300: Algebra II (3 credits)

Description

Rings: quotients rings, isomorphism theorems, prime ideals, maximal and of finite type, Zorn’s lemma, Cartesian products, Chinese remainder, Euclidean domains and single factorization, polynomial rings, key rings, irreducible and Eisenstein criterion. Body: body fractions, field extensions, algebraic extensions and minimal polynomials. Other selected topics.

MAT-2310: Number Theory (3 credits)

Description

Reminders: divisibility, unique factorization theorem, congruences and theorems of Fermat, Euler and Wilson. Quadratic Remains, Legendre and Jacobi symbols, quadratic reciprocity laws. Arithmetic functions, special numbers, distribution of primes. Diophantine equations. Continued fractions, algebraic numbers and transcendental numbers. Other selected topics.

MAT-3120: Complex Analysis (3 credits)

Description

Complex numbers. Analytic functions. Elementary functions. Cauchy. Cauchy formula and applications. Normal convergence. Power series. Laurent series. Residue calculation.

HST-2901: History of Mathematics (3 credits)

Description

Mathematics before the Greeks (Egypt and Babylon). The axioms of Euclid. Indian and Arabic mathematics. Analytic geometry. Calculus. Developments since 1800; Topics selected from: non-Euclidean geometries, set theory, modern axiomatic (Hilbert), number theory, introduction of algebraic structures, etc. Overview of recent developments.

MAT-3600: Graduation Project (3 credits)

Description

Preparation, writing and oral presentation of a project chosen from a list of available topics.

RULE 1-9 To 18 AMONG CREDITS

MAT-2330: Applied Modern Algebra (3 credits)

Description

Theory of finite fields and applications to linear codes: Code constructions, detection and error correction, Hamming codes, polynomial codes, cyclic codes. Power factorization algorithms and algorithms based on finite groups of properties; cryptography (RSA). Fast Fourier transforms and fast multiplication of polynomials. Introduction to Boolean algebra and applications to circuits. Theory of enumeration Polya; Applications to Combinatorics.

MAT-2410: Optimisation (3 credits)

Description

Notions of convexity. Lagrange multipliers and saddle point problems. Optimality conditions in the presence of constraints. Duality. Kuhn-Tucker problem. Numerical optimization methods for problems without constraints.

MAT-2420: Mathematical Modeling (3 credits)

Description

The purpose of this course is to improve the student’s ability to model problems in concrete situations. Many examples will be treated according to the following steps: determination and formulation of the problem, building a mathematical model, solving math problems inherent to the model chosen, explanation and interpretation of results.

MAT-2430: Introduction to fractals and dynamical systems (3 credits)

Description

Fractals conventional internal similarity. Similarity dimension. Fractal constructions: iterated function systems, L-systems. Length, area and size. Irregular shapes. Some notions on dynamic systems: fixed points, periodic points, stability, connections between discrete and continuous systems, phase space. Iteration of functions of one variable: bifurcation diagram, symbolic dynamics, chaos. Iteration of functions of a complex variable: Julia sets and Mandelbrot.

MAT-2500: Logic and foundations of mathematics (3 credits)

Description

Relationship between mathematical language and mathematical structures: mathématisant process. Propositional calculus and predicate calculus: syntax and semantics. Consequence and Deduction (syntactic and semantic). Origin and nature of the modern problem of the foundations of mathematics: the study of Frege and Russell systems. Properties of first order languages: theorems of completeness and compactness. Elements of model theory; applications, in particular to the non-standard analysis. First order theories: Peano axiomatic systems and Zermelo-Fraenkel. Incompleteness: Gödel’s theorems and Kirby-Paris.

MAT-2510: Math Problem Solving (3 credits)

Description

Standard techniques were used in the exhibit problem solving. This is how we will process of induction. Furthermore, using problems from the analysis, algebra, probability, geometry and applied mathematics, we will present how to approach different problems and reduce every problem to simpler problems. Moreover, we discuss the role of against-examples and the importance of properly raise issues.

MAT-2520: Themes mathematics for college education (3 credits)

Description

Mathematics Study and deepening of concepts related to teaching at the college level, particularly in computation, analysis, linear algebra and geometry. Limitations of mathematical techniques and concepts taught in college. Fractals and iterative systems and conical spheres Dandelin, number systems, thoroughness and reasoning. During Exploration taught in college programs. Using relevant software including GeoGebra and LaTeX.

MAT-2700: Selected Topics in Advanced Mathematics I (3 credits)

Description

This course will cover various topics in the field of advanced mathematics.

MAT-2710: Selected Topics in Advanced Mathematics II (3 credits)

Description

This course deals with a theme of advanced mathematics.

MAT-2920: Quality Management (3 credits)

Description

Modeling and formulation of optimization problems. Linear programming: simplex foundations, post-optimization, sensitivity analysis, duality, algorithms and dual primal-dual, flow problems in networks. Integer linear programming: simplex method, methods of truncation method successive subdivision, etc.

MAT-3130: Curves and surfaces (3 credits)

Description

Study of curves and surfaces whose “theorema egregium” and the Gauss-Bonnet theorem. Curves: length, curvature, torsion and osculating sphere. Areas: tangents, normal, basic forms, area, Gaussian curvature and mean curvature. Geodetic theory.

MAT-4000: Measurement and integration (3 credits)

Description

Introduction: explanation of the reasons for the introduction of Lebesgue integral. Measurable spaces. Integral: Integral simple functions, extension, monotone convergence theorem, Fatou theorem. Integrable functions. Classic examples (Lebesgue Lebesgue-Stieltjes, etc.). Dominated convergence theorem. Convergence modes. Breakdown of measures. Measures product: theorems of Tonelli and Fubini.

MAT-4120: Advanced Complex Analysis (3 credits)

Description

Holomorphic functions, principle of identity, the open application theorem, inverse function theorem, lemma Schwarz-Lindelöf principle Phragmén. Normal families. Univalent functions, theorems of Riemann and Koebe. Runge’s theorem. Infinite products. Riemannian metric, Schwarz-Pick theorem, curvature, theorems of Ahlfors, Picard and Montel.

MAT-4150: Errors and differential forms (3 credits)

Description

Differential forms in Euclidean space, exterior derivative, Poincaré lemma. Differential varieties. Integration of differential forms, Stokes theorem, applications.

MAT-4200: Advanced Probability (3 credits)

Description

Reminder on the measure theory. Random variable, distribution, hope. Independence. Law of all or nothing Kolmogorov. Strong convergence and law of large numbers. Weak convergence theorem and the central limit.

MAT-4300: Algebra III (3 credits)

Description

Vector spaces, R-modules, quotient modules, homomorphisms. Exact sequences, complex modules and examples of functors: tensor product, Hom. Representation theory of finite groups. Introduction to language classes.

MAT-4400: Numerical linear algebra (3 credits)

Description

Typical problems when numerical linear algebra is a fundamental tool: discretization equations problems with partial derivatives, regression, factor analysis, etc. Methods for solving linear systems: direct methods, iterative methods, conjugate gradient method preconditioned. Troubleshooting the least squares and generalized inverse calculation. Applications. Calculation of eigenvalues and vectors. Method powers and QR method. Singular value decomposition and applications to generalized inverse. The course will include practical case analysis using the most common software.

MAT-4410: Numerical Solution of ODE and PDE (3 credits)

Description

Approximation of functions. Numerical integration. Numerical methods for systems of differential equations. Finite differences for PDEs.

MAT-4500: Topology (3 credits)

Description

General Topology and continuous functions. Compactness and connectedness. Countability and separation axioms: Hausdorff spaces, regular, normal; Urysohn lemma; metrizable spaces. Algebraic Topology: fundamental group, covering space. Fundamental group of the circle of the sphere. Retraction and fixed points. Coating areas: universal cover. Applications

STT-4700: Random Processes (3 credits)

Description

Probability and conditional expectations. Markov chains in discrete time Markov chains with continuous time. Toughness, aperiodicity, recurrence, invariant measure, ergodicity. Some classic models: random walks, branching processes, Poisson processes, birth and death process, queuing models. Introduction to Brownian motion.

RULE 2-6 To 15 AMONG CREDITS

Actuarial ACT-1000: Introduction to Actuarial I (3 credits)

Description

Notions of risk: insurable, uninsurable. Risk types: life, non-life; short and long term. Life insurance contracts: general principles: traditional insurance, universal insurance; annuities; selection; examples. Non-life insurance: general principles; auto, home, responsibility; classification; examples. Health insurance contract: general principles; private insurance; selection; examples. Reinsurance concepts purpose; types of contracts; examples.

ACT-1001: Financial Mathematics (3 credits)

Description

Various measures of interest. Value equation. Annuities certain, constant payment or not. Repayment of a loan: progressive damping, sinking funds, possibilities of prepayment and refinancing. Evaluation of bonds and shares. Various performance measures. Duration and convexity. Matching and immunization.

ACT-2001: Introduction to Actuarial Science II (3 credits)

Description

Application of stochastic simulation. General risk management. Introduction to life insurance rates: mortality table, unique net premium, net level premium reserve. Introduction to Non-Life Insurance Rating: frequency and severity; applications; pricing of the premium; deductible and selection changes; Unlike these stages between life insurance and non-life insurance.

ACT-2004: Actuarial life Mathematics I (3 credits)

Description

Survival functions on a head. Mortality measures. Insurance benefits and annuity: discrete approach, continuous approach, particular cases. Calculation of pure premiums; discreet approach, continuous approach, annual bonus, special cases.

ACT-2005: Casualty Actuarial Mathematics I (3 credits)

Description

Sinitres distribution and frequencies; introduction to bootstrap; semi-parametric models; applications with numerical examples.

ACT-2007: Life Actuarial Mathematics II (3 credits)

Description

Reserves for basic contracts. Multi-decay models. Basic multi-decay models applications. Models with two lives: a joint life and last survivor.

ACT-2008: Casualty Actuarial Mathematics II (3 credits)

Description

Credibility theory: classical and Bayesian approaches, models of Buhlmann and Buhlmann-Straub, estimation of structural parameters. Introduction to pricing and provisioning in general insurance: classical methods and presentation in a formal setting using the generalized linear models.

Oral and Written Communication

COM-1500: Oral communication in public (3 credits)

Description

This course aims to develop the ability to communicate orally in a heterogeneous group. Study of verbal and nonverbal components required for oral communication quality. Action and oral feedback guided by the teacher, with the logistical support of the video. Note – This course aims to consolidate the general knowledge of French and knowledge of university-level French.

EDC-1001: Research, Analysis and dissertation (3 credits)

Description

The general objective of this course is to enable students to acquire the skills required to produce a dissertation of a dozen historical pages in his field of study. This course can therefore cover several academic areas: archeology, political science, social sciences, translation, business administration, management, law, policy, education, pure sciences. This course can therefore be relevant to any program that requires the student, at one time or another, the production of a long process that involves the history of a discipline or field of study . Specifically, the student must develop skills to establish a problematic, a hypothesis and a demonstration plan to differentiate factual information of a copyright argument, writing complete paragraphs, to develop text coherent and structured, and many other aspects that are addressed in the training manual for this purpose.

ENG-1914: Scientists Communications (3 credits)

Description

The course is for students in scientific or technical programs who wish to acquire an effective method to communicate complex content. It focuses on the analysis and synthesis of text and includes an introduction to science. It shows also how to take into account various communication situations. Note – This course aims to consolidate the general knowledge of French and knowledge of university-level French.

PHI-1900: Logical Principles (3 credits)

Description

This course aims to make known some of the tools of thought and above all to show how to use them to better arrange the existing knowledge or those under development. We learn to analyze a text or a point of view, to bring out the essential, defining the concepts involved, to distinguish and evaluate the arguments involved. Such training is proving an asset to profitably address any field of study. It also assists in drafting more precise and coherent texts. As this is a basic course requires no previous training in logic. It may be followed by people in any field, as well, of course, by those who are enrolled in a philosophy program.

BIO-1902: Sustainable Development: Introduction to Genetic Analysis (3 credits)

Description

Mendelian genetics. Chromosome theory. Genetic linkage and chromosome mapping. Cytogenetics. Structure and function of DNA. DNA manipulation. Transgenesis. Regulation of gene expression. Mechanisms of genetic change. Genomics. Quantitative genetics. Population genetics. Ethics and genetics.

DDU-1000: Foundations for Sustainable Development (3 credits)

Description

This introductory course to sustainable development is for all undergraduate student. It is to provide an introduction to the concept of different sizes and the implementation of sustainable development tools. It allows the student to acquire the basic elements of a general reflection on sustainable development, which takes into account its many ambiguities and difficulties in its operationalization. In addition, this course encourages thinking about the tools necessary for his apprehension as social project. This interdisciplinary course is delivered remotely to autumn sessions, winter and summer. This course is mandatory sustainability profile.

DRT-1721: Introduction to Environmental Law and Sustainable Development (3 credits)

Description

Introduction to environmental law in the context of current and future environmental challenges. Overview of the main legal instruments in Haiti to fight against environmental pollution and climate change, preserving biodiversity and implement sustainable development. Study of administrative appeals, civil and criminal. Study of authorization schemes, procedures of public review of the impacts and administrative appeals, civil and criminal to the public and to public administration.

ECN-1150: Environmental Economics (3 credits)

Description

Economic analysis, theoretical and practical aspects of environmental problems and solutions that may be proposed: pollutant emissions control policies (taxation of pollutant emissions, tradable pollution rights, regulations currently in use, etc.); proposals economists on monetary valuation of benefits and costs related to environmental protection; current issues, such as the greenhouse effect.

GCI-3001: Environmental Impacts (3 credits)

Description

This course helps to learn the impact studies and develop methodological tools for such studies. It includes a review of federal and provincial impact assessment and their regulatory process; the review of available methods, types case studies of recent projects; the identification and management of conflicts of environmental impacts. Notions of environmental auditing.

MNG 2110: Sustainable development and management organizations (3 credits)

Description

This course’s main objective is to provide conceptual and practical tools to understand and efficiently integrate the concept of sustainable development in organizations. The foundations and practical applications of this concept will be apprehended using various examples and an interdisciplinary perspective.

POL-2207: Environmental Policies (3 credits)

Description

The course objective is to introduce students to environmental issues from the perspective of policy analysis and public administration. The evolution of ecological thinking. The appearance of the main environmental issues and problems in contemporary societies. The instruments and management mechanisms at national and international level. The role of social forces. Quebec and Canadian dimension of environmental policies. Foreign experiences.

SOC-2114: Environment and Society (3 credits)

Description

Study of the relationship between nature and societies. Representations of nature. Genesis of the ecological thought. Environmental issues: water, forests, air, ocean energy. Science and politics of global environmental problems: climate change, biodiversity. The environmental movement: origin, diversification, actions and impacts. Environmental policies and sustainable development.

Economic

ECN-1000: Principles of Microeconomics (3 credits)

Description

Scarcity, choice and opportunity cost. What to produce, how to produce and for whom to produce. Factors determining the demand function and supply for a product. Price and equilibrium quantity. The laws of supply and demand. Concept of elasticity. Government intervention. Consumer choices: preferences and budgetary constraints. The choice of companies: profit and production function. Cost functions. Price competitive markets and monopoly markets.

ECN-1010: Principles of Macroeconomics (3 credits)

Description

The macroeconomic objectives: full employment, price stability, balance of the balance of payments. National Accounts. P.I.B. balance and full employment. Roles of the currency and financial institutions. The State and aggregate demand. Macroeconomic objectives and internal policies. The constraints posed by the opening of the economy. Keynesians and monetarists. The difficult art of macroeconomic policy. Looking for a consensus on the desirability and means of state intervention.

ECN-2000: Price Theory I (3 credits)

Description

The focus is on the determination of prices of final goods and services in the economy and on the allocation of resources in the production of these. The course revolves around the concepts of supply and demand in the goods market, which allows grouping of consistent and analytically different economic variables at play.

ECN-2010: Macroeconomic Theory I (3 credits)

Description

Determination of national income, employment, prices, interest rates and the exchange rate in an aggregate context; Explicit model with four markets: goods and services, money, work, foreign currencies. North American macroeconomic policy; importance of the external sector of the Canadian and Quebec economies. Macroeconomic analysis using models. National Accounts.

ECN-2020: Price Theory II (3 credits)

Description

Pricing and employment of factors of production in the economy. Variables that influence the demand and supply of factors of production in the company, the industry and the economy. Releasing the hypothesis of perfect competition: monopoly, monopolistic competition, oligopoly. Edgeworth box, Pareto optimal. Demonstration of two fundamental theorems of welfare theory.

ECN-2030: Macroeconomic Theory II (3 credits)

Description

Key determinants of consumption, investment, government spending, imports, exports. Supply and demand for money. Short term production function. Economic developments compared wages and profits. Sources of inflation and unemployment. Theory of economic growth. Factors of instability and state intervention in the economy modes.

ECN-3000: Introduction to Econometrics (3 credits)

Description

The formulation of hypotheses from theories about socioeconomic phenomena and the use of econometrics to verify these hypotheses. The focus is on the significance and practical significance of econometric results rather than their formal mathematical proofs.

ECN-4100: Econometrics (3 credits)

Description

Multiple regression matrix writing emphasizing the model assumptions. Special problems of multicollinearity, non-spherical errors and autocorrelation. Generalized method of least squares, the use of instrumental variables, the lag model and the identification problem in the simultaneous equation models.

Education

ENS-1001: Adolescence (3 credits)

Description

This course takes an ecological perspective and discusses theories and research on adolescent development. It deals with the physical, psychosexual, cognitive, and social identity of adolescents in a school-optical response. He is also interested in the role of agents of socialization and education: teachers, peers, parents and adults other than parents (eg. Tutors and mentors). It explores some of the more unusual problems such as suicide, anorexia and social reality of adult continuing education.

ENS-1002: Social aspects of education (3 credits)

Description

Dynamic analysis of school-society relations and the social dynamic present in school and in the classroom. Cultural, political, economic education system. Educational challenges of pluralism in schools. Social functions of the school, social and educational issues, interdependent phenomena of relative autonomy, power relations in the action systems.

ENS-2001: Students with behavioral difficulties (3 credits)

Description

This course has three objectives. The first is to convey to the student the knowledge on the study of behavior problems in adolescent and adult populations. The second is to allow the student to use this knowledge to work with school professionals in the identification and assessment of students with symptoms of a behavior problem. The third is to acquaint the student with the main interventions used in school classrooms. At the end of this course, students will understand the importance of offering individualized intervention plans for students with behavioral problems, while being able to take a critical look at the development of these action plans.

NS-2100: Evolution of ideas and teaching practices (3 credits)

Description

Introduction to the evolution of ideas and teaching practices, from antiquity to the present.

PHI-3900: Ethics and Professionalism (3 credits)

Description

Professionals today are faced with situations that require ethical skills and knowledge that go beyond technical knowledge specific to their area of expertise. On the one hand, professionalization is a changing phenomenon, which requires a reflection on the meaning of work and more specifically on professionalism. Furthermore, although the professional practice is regulated by a code of ethics, the professional is asked to have a sense of ethical responsibility. Through case studies and analysis of the various issues related to professionalism, the course offers an ethical reflection on professional practice and the conditions in which this practice occurs.

POL-1005: Introduction to International Relations (3 credits)

Description

Study of the international system; historical formation and ideological foundations; types of systems and transformations; Contemporary system; conflict process; Cooperation Process; transnational forces; major topics of current international debates; diplomacy and foreign policy.

POL-2312: Haiti International Relations (3 credits)

Description

This course provides an introduction to international relations of Haiti. It focuses on the approaches and theories for understanding the behavior of Haiti on the international stage. The main internal, external and institutional factors that influence the Haitian foreign policy are studied. Addressed themes: Haiti interventions abroad, relations with the US, security and the defense of the country, international development assistance and report that Haiti has with international organizations like the UN and NATO.

SOC-1003: Training and development of contemporary Haiti (3 credits)

Description

This course outlines a historical interpretation of the Haitian society. Then linked together a series of lectures on selected topics: the nation, the demographic issue, urbanization, cultural pluralism, women’s, labor, etc.

SOC-2111: Science and Society (3 credits)

Description

This course focuses on the relationship between science and society from the point of view of history and sociology. It examines the circumstances of the emergence of Greek science, and those surrounding the birth of modern science. It presents the sociological analysis of the nature and function of the current science.

SOC-2120: Sociology of technological innovation (3 credits)

Description

Context, processes and impacts of technology innovation. Science and technology. Explain innovation. States and companies in research and development. Science and technology policies. Socio-technical controversies: large dams; biosciences and biotechnology; new information technologies; nanotechnology. Managing technological risks. High reliability organizations. Social technology assessment.

Informatics

GIF-1001: Computers: structure and applications (3 credits)

Description

This course presents the internal architecture of the computer and the organization of these key elements. He is preparing for the operation of the computer in engineering problems such acquisition and data processing, industrial control and device management. In order to release the physical and logical vision, he mainly uses assembly language. The microcomputer compatible PC serves typewriter in the discussion of various concepts and in practical work.

GIF-1003: Advanced C ++ Programming (3 credits)

Description

Oriented programming in C ++ object. Elements of syntax and semantics. Implementation of classes: encapsulation, methods and class attributes. Overloading methods and operators. Notion of contract and unit test. Programming standards. Inheritance, polymorphism and class hierarchy. Memory management. Error handling and exceptions. Standard library C ++ (STL).

IFT-2001: Operating Systems (3 credits)

Description

History and development. Roles, components and function of an operating system. Protection and system performance. Necessary physical structures. Processes and allocation of CPU. Memory management and virtual memory. Secondary memory and cache. Management of inputs / outputs. Filesystems. Process of coordination and dead ends. Concurrent programming. Case Study: UNIX, DOS, VMS, VM, WINDOWS.

IFT-2002: Theoretical Informatics (3 credits)

Description

Introduction to the theory of abstract machines and formal languages. Classification of abstract machines: finite automata, pushdown automata, Turing machine. Classification of languages: regular, non-contextual, recursive recursively enumerable, not recursively enumerable. Grammar: syntax, Chomsky classification, relationships with abstract machines and languages. Theory sequences. Finite sets, infinite, countable and uncountable.

IFT-2003: Artificial Intelligence I (3 credits)

Description

Definition and applications of artificial intelligence. Knowledge representation formalisms: semantic networks, predicate logic, clausal logic, etc. An artificial intelligence language Prolog. Problem solving techniques. Applications: games, planning, natural language processing, expert systems. Programming work done in Prolog.

IFT-2008: Algorithms and Data Structures (3 credits)

Description

Order concepts: behavior best case, average case and worst case. Notion of abstract and modular type. Generic programming. Classic data structures: lists, stacks, queues (with and without priority), the trees, graphs, dispersion tables and binary heaps. Sorting algorithms.

IFT-3000: Programming Languages (3 credits)

Description

Programming paradigms. Lambda calculus, semantic dynamic, static semantics and type inference. Functional programming, functional abstraction and application. Object-oriented programming, classes, objects, messages and legacy (single and multiple). Parallel and distributed programming. Modularity and structuring. ML languages, Objective CAML, SmallTalk, Java and Concurrent ML.

IFT-3001: Design and Analysis of Algorithms (3 credits)

Description

Analysis of the effectiveness of the algorithms: asymptotic analysis, analysis and worst case average. Asymptotic notation, recurrences resolutions. Strategies in the design of algorithms: greedy algorithms, “divide and rule”, “decreasing rule”, dynamic programming. Probabilistic algorithms. Elements of computational complexity.

IFT-3100: Computer Graphics (3 credits)

Description

Introduction to computer graphics concepts. Construction of a graphics package. Graphics rendering pipeline concept. Reminder of basic notions of vector calculus and geometry and their use in computer graphics. Elementary geometric objects and basic geometric modeling. Geometric transformations. Camera and 3D scene setting. Cutting a scene. Illumination of objects. Generating texture. Practical work in C ++ with OpenGL.

IFT-4102: Approach artificial intelligence agent (3 credits)

Description

Intelligent agents. Problem solving by exploring: classical approaches, informed and adversity. Constraint satisfaction problems. Machine learning: supervised (decision trees, ensembles, statistical approaches, neural networks, etc.), unsupervised and reinforcement. Probabilistic reasoning and decision making (simple and complex). Applications of artificial intelligence.

Physics

PHY-1000: Introduction to astrophysics (3 credits)

Description

The course, which is open to physics students and students with basic scientific knowledge (college level science program of nature), is a review of basic concepts and recent discoveries of modern astrophysics. Topics include: planetary motion, solar and lunar phenomena, telescopes, classification and evolution of stars, compact objects (white dwarfs, pulsars and black holes), the Milky Way and other galaxies, quasars and cosmology.

PHY-1003: Mechanics and Relativity (3 credits)

Description

Non Galilean reference systems. Special relativity. Kinematic: postulates, Lorentz transformations, concept of four-vector Minkowski diagram, velocity addition. Dynamic: covariance, quadrivector energy-momentum, collisions. Benchmarks accelerated linearly or in rotation. Introduction to rigid body dynamics.

PHY-1006: Quantum Physics (3 credits)

Description

This course aims to develop the student a solid understanding of the fundamental concepts of quantum physics. Thermal radiation and Planck’s postulate. The photon and corpuscular aspect of radiation. The postulate of de Broglie wave aspect and the particle. The Heisenberg indeterminacy relations. The Bohr atomic model. Quantum mechanics and the Schrödinger equation. Applications of the Schrödinger equation in some simple potentials: free particle, walking, barrier and potential well. The hydrogen.

PHY-1007: Electromagnetism (3 credits)

Description

Electrostatic field: Coulomb’s law, Gauss’ law, electric potential. Electrostatic problems of solutions of Laplace equations and Poisson. Stationary electric currents. Electrostatic phenomena in the dielectric. Magnetic field: vector potential, Biot-Savart law, magnetic energy. Non-stationary field: Faraday’s law, Maxwell’s equations.

PHY-1902 : Astronomy: a guided tour of the universe (3 credits)

Description

This general education course is for the student who is not enrolled in a science and engineering program. No advance in science or mathematics is required: physical concepts are introduced progressively. Celestial phenomena: constellations, seasons, tides, eclipses, time measurement. Tools of astronomy: light, matter, astronomical instruments. Stars: Types, birth, evolution, death, pulsars, black holes, the sun. Solar system: planets, moons, asteroids, comets. Galaxies: Milky Way interstellar matter, quasars. Life on Earth and in the Universe. Cosmology: expansion of the universe, big bang, large-scale structure.

PHY-2001: Electromagnetic waves (3 credits)

Description

Review of Maxwell’s equations and boundary conditions. Solution of Maxwell’s equations in vacuum, in a dielectric medium in an ionized gas in a conductive medium. Plane-wave planar interfaces: normal incidence, oblique incidence. Optical applications: antireflection layer, Brewster angle polarizer. Notions on transmission lines. Metal waveguides: bi-planar, rectangular and circular. Planar dielectric waveguides. Solutions of Maxwell’s equations with a source term: radiation. Dipole antenna.

PHY-2100: Space Science (3 credits)

Description

This course is for students enrolled in science and engineering program or geomatics. It is an introduction to space research and the specific problems of space. Space probes and artificial satellites. The space environment and use. Terrestrial and planetary atmospheres atmospheric luminescence. Cosmic energy sources. Astrodynamics elements. Space exploration. Scientific and technical programs.

RULE 3-0 9 AMONG CREDITS TO:

Statistics

STT-1100: Introduction to the main statistical software (3 credits)

Description

This course introduces the student to the R and SAS software, so that it can perform exploratory analyzes of data sets. The student learns to design and execute programs R and SAS to capture, read, import and manipulate data, to calculate univariate and multivariate descriptive statistics, generate graphs, to simulate random variables and adequately include statistical outputs in a report.

STT-1400: Statistical Quality Assurance (3 credits)

Description

Quality problem. Methods of description of the change: graphical and numerical representations, inferential techniques, ability study of a process. Methods of controlling the variation: in-process control, control over reception. Methods of reducing the variation: the problem of the reduction, full 2k factorial plans factorial design 2k-p fractional.

STT-2100: Regression (3 credits)

Description

Simple regression: point estimates and confidence intervals of the various parameters. Forecast. Study of residues. Linearity test. Linearization. Joint estimation. Multiple Regression: point estimates and confidence intervals for the various parameters. Tests on the regression coefficients. Test adjustment. Multicollinearity. Reparameterization. Dummies. Description and illustration of polynomial regression methods, weighted, logistic and nonlinear. Introduction to instrumental variables.

STT-2200: Data Analysis (3 credits)

Description

Theory and application of four classical data analysis multivariate methods: principal components analysis, correspondence analysis, discriminant analysis. Classification. Learning software facilitating the use of these methods.

STT-2300: Variance analysis (3 credits)

Description

Multivariate normal distribution. Lois random quadratic forms. Cochran’s theorem. One-factor model. Multiple comparisons. Two-factor model. Interaction. Studies shots of experience: completely random design, randomized block, shared plots. Using SAS.

STT-4100: experiences Planning (3 credits)

Description

Structure of a statistical experiment: concepts of experimental error, randomization, blocking and repetition. Links with regression models; analysis of covariance. Unbalanced factorial schemes. Prioritized plans. Plans incomplete block. Response surfaces. Using SAS.

STT-4400: frequency tables analysis (3 credits)

Description

Frequency tables of two variables: proportions, odds ratio and relative risk, tests and measures of association, ordinal variables, paired data. Frequency tables with three variables: marginal association and conditional association, Simpson’s paradox. Generalized Linear Models: Poisson regression and binary logistic regression, conditional, ordinal and multinomial variable selection and measurement of model fit. Analysis of data using statistical software.

STT-4500: Non parametric statistics (3 credits)

Description

Problems to two samples: rank tests for a translation parameter. Problems to a sample: signed rank tests for a location parameter. Comparison of k treatments: Kruskal-Wallis, contingency table, Friedman test, Cochran, etc. Trend tests and independence tests using the ranks. Introduction to “bootstrap”.

STT-4600: Sampling (3 credits)

Description

Designing a questionnaire. Simple and stratified sampling techniques. Treatment of non-response. Methods and the quotient of the regression for the use of additional data. Cluster sampling techniques, systematic and multi-stage. Sampling weight.

STT-4630: Time series (3 credits)

Description

Notions of stationary and non-stationary processes. Description of ARMA and ARIMA models. Autocorrelations and partial autocorrelations. Methods for estimating conditional least squares, moments and maximum likelihood. Properties of estimators and tests. Forecasts and adequacy of a model. Special topics: seasonal patterns, random walk hypothesis, cointegration.

OTHER REQUIREMENTS PROGRAM (3 CREDITS)

RULE 1-3 CREDITS

Pass the course ANL-2020 Intermediate English II or English classes higher. Students who acquired the Advanced English II level can substitute the English course with a course of another modern language.

POSSIBILITY OF CHOICE STUDY PROFILES

Distinction Profile

The profile distinction is offered to the best students. It consists of a fixed arrangement of 12 credits (minimally 6 graduate credits) between the direction of a degree program and the direction of a master’s program. The graduate courses are contributory bachelor and master. The Bachelor of Mathematics offers distinction profile with the following programs:

Math Masters

Math Mastery – with Memory

The student is asked to contact the program director to determine the conditions of admission to this profile.

The student should have acquired two thirds of the program credits and have an average program of equal or greater to 3.67 / 4.33.

Course Information
  • Course Id:MAT
Instructors