The Professional Master's Degree in Mathematics in a National Network (PROFMAT) is a semi-attendance course, with national offer, carried out by a network of higher education institutions, in the context of the Open University of Brazil (UAB), and coordinated by the Brazilian Society of Mathematics (SBM).
PROFMAT/IMECC classes are held weekly, on Fridays and possibly also on Saturdays. In particular, during the first year of the course, all assessments are carried out on Saturdays.
PROFMAT aims to serve Mathematics teachers working in basic education, especially in public schools, who seek to improve their professional training, especially on the relevant mathematical content for their teaching activities.
The medium-term objective of the program, which operates on a large scale, is to have a substantial impact on the mathematical training of teachers throughout the country.
The program is coordinated by the Management Council and the National Academic Commission, subordinated to the Board of Directors of the Brazilian Society of Mathematics (SBM) and is carried out by the Academic Commissions of the Associated Institutions.
(Text adapted from http://www.profmat-sbm.org.br/index.php/organizacao/apresentacao)
MN021 (from 2020)
Completion of Master's Thesis
MN011 – Real Numbers and Functions
Sets. Natural Numbers. Cardinal numbers. Real Numbers. Related Functions. Quadratic Functions. Polynomial Functions. Exponential and Logarithmic Functions. Trigonometric Functions.
MN012 - Discrete Mathematics
Natural Numbers. The Method of Induction. Progressions. Recurrences. Financial math. Combinatorial Analysis. Probability. Medium and Drawers Principle.
MN013 – Geometriy
Basic Geometrical Concepts. Congruence of Triangles. Geometric Places. Proportionality and Similarity. Areas of Flat Figures. Trigonometry and Geometry. Basic Concepts in Spatial Geometry. Some Simple Solids. Convex Polyhedra. Volume of Solids.
MN014 - Aritmethic
The Integers. Induction Applications. Division into Integers. Representation of Integers. Euclid's Algorithm. Applications of the Greatest Common Divider. Prime numbers. Special numbers. Congruences. The Euler and Wilson Theorems. Linear Congruences and Residual Classes. Quadratic Congruences. Notions of Cryptography.
MN021 - Problem Solving
Problem Solving Strategies. Basic Mathematics and Logical Reasoning Techniques: Reduction to the Absurd, Induction Principle, Analysis of initial cases, Pigeon house principle, Extreme case principle. Problems involving Real Numbers and Functions: Discrete Mathematics, Geometry, Arithmetic and Algebra. Analysis of exams and tests: ENEM, Vestibular, Olympics and similar.
MN022 – Calculation Fundamentals
Real Number Sequences. Role Limit. Continuous Functions. Derivation. Integration.
MN023 - Analytical Geometry
Coordinates in the Plan. Vectors in the Plan. Line Equations in the Plan. Relative Position between Lines and Circles and Distances. Ellipse. Hyperbole. Parable. General Equation of the Second Degree in the Plan. Parameterized Flat Curves. Coordinates and Vectors in Space. Internal Product and Vector Product in Space. Mixed Product, Volume and Determinant. The Line in Space. The Plan in Space. Systems of Linear Equations with Three Variables. Distance and Angles in Space.
MN024 – Completion of course work
Discipline dedicated to supporting the elaboration of work on a specific topic relevant to the Mathematics curriculum in Basic Education and that has an impact on didactic practice in the classroom. Each work is presented in the form of an expository class on the theme of the project and a written work, with the option of presenting technical production related to the subject.
MN031 – Topics in the History of Mathematics
Mathematics in Babylon and ancient Egypt. Greek Mathematics up to Euclid. Greek Mathematics after Euclid. Al-Khwarizmi, Cardano, Viète and Neper. The New Mathematics of the 17th Century. Functions, Real and Complex Numbers.
MN032 – Topics in Number Theory
Fundamentals. Powers and Congruences. Multiplicative Functions and Möbius Inversion Formulas. Continuous Fractions. Nonlinear Diophantine Equations.
MN033 - Introduction to Linear Algebra
Linear Systems and Matrices. Matrix Transformation and Systems Resolution. Vector Spaces. The R3 Space. Linear Transformations. Linear Transformations and Matrices. Spaces with Internal Product. Determinants. Diagonalization of Operators.
MN034 - Topics in Differential and Integral Calculus
Real Number Series. Taylor Polynomials. Functions of n Variables. Partial derivatives and Gradient. Critical Points of an n-Variable Function. Multiple Integral.
MN035 – Mathematics and Current Affairs
This subject should present an overview of the presence and usefulness of Mathematics in everyday life. Some suggestions for topics to be studied: Mathematics and Music. Sounds and Sound File Compression. Passwords used in Banks and on the Internet. Codes. The Geometry of the Terrestrial Globe. GPS operation. The Mathematics of Barcodes. Conics Applications. Other topics related to technological innovations.
MN036 – Computational Resources in Mathematics Teaching
The use of Calculator in Mathematics Teaching. Spreadsheets. Graphic environments. Dynamic Geometry Environments. Algebraic Computing Systems. Distance learning. Electronic Searches, Word Processors and Hypertext. Criteria for Selection of Computational Resources in Mathematics Teaching.
MN037 – Mathematical Modeling
Conceptual Aspects of Modeling. Optimization in Mathematical Modeling. Differential and Difference Equations in Mathematical Modeling. Probability and Statistics in Mathematical Modeling. Graph Theory in Mathematical Modeling. Mathematical Modeling in Teaching.
MN038 – Polynomials and Algebraic Equations
The Complex Numbers. The Geometry of the Complex Plane. Basic Properties of Polynomials. Polynomial Factorization. Algebraic Equations. Constructions with Ruler and Compass. The Hypercomplex Numbers.
MN039 - Spatial Geometry
Incidence. Angles and Relative Positions between Lines and Planes in Space. Angles in Space. Dihedral, Trihedral and Polyhedral angles. Prisms, Cylinders, Pyramids, Cones and Spheres. Polyhedra. Plato's Polyhedra. Euler's formula. Volumes.
MN040 – Math Topics
Disciplina sem ementa fixa, com programa a ser proposto por iniciativa de cada Instituição Associada.
MN041 – Probability and Statistics
The Nature of Statistics. Treatment of Information. Frequency Distributions and Graphics. Measures. Basic Concepts in Probability. Conditional Probability and Independence. Discrete and Continuous Random Variables. Cumulative Distribution Function. Hope and Variance of Random Variables. Bernoulli, Binomial and Geometric models. Uniform Model and Normal Model. Asymptotic Distribution of the Sample Mean. Introduction to Statistical Inference.
MN042 - Educational Assessment
The National Educational Assessment Exams. The National Higher Education Assessment System. What is Item Response Theory? Estimation of Parameters and Proficiencies in TRI. Item Construction Engineering. Assessment as a Means to Regulate Learning.
MN043 - Numerical Calculation
Introduction to mMthematic Modeling. Model building. Examples of Finite Difference Models and Growth Model. Roots of Equations. Bisection Methods. Fixed Point and Newton. Curve adjustment. Linear and Quadratic Approximations. Polynomial Interpolation. Least Square Adjustment. Derivation and Numerical Integration.