Continuing Education Center Pre-University Courses Mathematics

Mathematics

1. The IUT pre-university mathematics curriculum offers its students chances to study mathematics more thoroughly and systematically, supplementing their high school class work.

2. The pre-university courses in mathematics are designed to help students to understand fundamental concepts and work out more challenging problems.

3. The IUT pre-university mathematics program offers three levels of curriculum depending on the students’ mathematical knowledge and problem-solving abilities.

Basic Level

– The basic level is designed for high school students with a working knowledge of about 1th or higher grade mathematics.

– In particular, students who register at this level should know in advance how to manipulate real numbers and polynomial expressions, draw graphs of linear, quadratic and trigonometric functions, understand geometry on Euclidean plane, solve quadratic equations, and prove mathematical statements from a given set of conditions, etc.

– The curriculum at this level provides the students with fundamental mathematical concepts including complex numbers, matrices, exponents, logarithms, sequence of numbers, and infinite series and basic techniques in calculus involving polynomial functions only

– The courses in the basic level will help students to progress to the intermediate or advanced level.

№	Subject	Contents
1	Complex numbers	Definition of complex numbers, their additions, multiplications, polar form r(cos a + i sin b)
2	Matrices and their operations	Definition of matrices, their additions and multiplications, multiplication of matrices with a real number, and other properties
3	Matrices and system of linear equations	Inverse matrix of matrix, formula of inverse matrix for a 2×2 matrix, Use of matrices to solve system of 2 linear equations with 2 variables
4	Exponents	Manipulation of exponents and n-th root, how to define a real power of a positive real number
5	Exponential functions	Properties of exponential functions and their graphs
6	Logarithms	Definition of a logarithm, common logarithm, characteristic, mantissa
7	Logarithmic functions	Properties of logarithmic functions and their graphs
8	Arithmetic progressions	Definition of a sequence and arithmetic progressions
9	Geometric progressions	Definition of a geometric progressions
10	Other sequences	Progression of differences and other type of sequences
11	Mathematical induction, limits of Sequences	Mathematical induction, intuitive introduction to limit of a sequence
12	Infinite series	Partial sum and infinite series, geometric series
13	Mid-term examination
14	Solving equations	Solving rational and irrational equations
15	Solving inequalities	Solving cubic, quartic and rational inequalities
16	Trigonometric functions	Manipulation of trigonometric functions using various formulas
17	Limits of functions	Intuitive understading of limits of a function in terms of shape of the graph of a function
18	Continous functions	Definition of a continuous function, intermediate value theorem, extreme value theorem
19	Derivative and differentiation	Definition of a derivative, differentiation of polynomial functions, sum and product of two functions
20	Tangent lines to a curve	Application of derivative to find the tangent line to a curve, increasing and decreasing functions
21	Derivative and graph of a function	Many worked out examples of graph drawing of cubic or quartic polynomial functions using differentiation
22	Moving particle, velocity, acceleration	Application of derivative to physics of a moving particle.
23	Anti-derivative (Indefinite integral)	Definition of indefinite integrals and formulas for indefinite integral of polynomial functions
24	Definite integral	Definition of definite integral and fundamental theorem of calculus
25	Areas and other applications of integral	Computation of area enclosed by curves, how to find a position of a moving particle when its velocity is known
26	Term-end examination

Intermediate

– The intermediate level is designed for high school students with a working knowledge of 2nd or higher grade mathematics.

– The courses in this level provide students more advanced topics in high school and prepare them to go on to the advanced level seamlessly.

– The intermediate level differs from the basic level in that it deals with trigonometric, exponential, logarithmic functions and utilize chain rule in calculus contents whereas the basic level only deals with polynomial functions.

№	Subject	Contents
1	Complex numbers	Definition of complex numbers, their additions, multiplications, polar form r(cos a + i sin b)
2	Matrices and their operations	Definition of matrices, their additions and multiplications, multiplication of matrices with a real number, and other properties
3	Matrices and system of linear equations	Inverse matrix of matrix, formula of inverse matrix for a 2×2 matrix, Use of matrices to solve system of 2 linear equations with 2 variables
4	Exponents and exponential functions	Manipulation of exponents and n-th root, how to define a real power of a positive real number, graphs of exponential functions
5	Logarithms and logarithmic functions	Definition of a logarithm, common logarithm, characteristic, mantissa, graphs of logarithmic functions
6	Arithmetic and geometric progressions	Definition of a sequence, arithmetic progressions, and geometric progressions
7	Other sequences and mathematical induction	Progression of differences and other type of sequences, how to prove a theorem using a mathematical induction
8	Limits of Sequences and infinite series	Intuitive introduction to limit of a sequence, infinite series, geometric series
9	Solving equations	Solving rational and irrational equations
10	Solving inequalities	Solving cubic, quartic and rational inequalities
11	Trigonometric functions	Manipulation of trigonometric functions using various formulas
12	Trigonometric equations	Solving equations involving trigonometric functions
13	Mid-term examination
14	Limits of a function	Intuitive understading of limits of a function in terms of shape of the graph of a function, limits of sum, product, quotient of 2 functions
15	Continuous function	Definition of a continuous function, intermediate value theorem, extreme value theorem
16	Derivative and differentiation	Definition of a derivative, differentiation of polynomial functions, sum and product of two functions
17	Differentiation techniques	Differentiation of trigonometric functions, exponential functions
18	More differentiation techniques	Chain rule, differentiation of inverse functions
19	Application of derivative	Concavity, many worked out examples of graph drawing of various functions using its first and second derivative
20	Anti-derivative (Indefinite integral)	Definition of indefinite integrals and formulas for indefinite integral, integration by parts, integration by substition
21	Definite integral	Definition of definite integral and fundamental theorem of calculus
22	Areas and other applications of integral	Computation of area enclosed by curves, motion of a particle (position, velocity, acceleration)
23	Basic combinatorics and binomial theorem	Permutations, combinations, binomial theorem
24	Probability, conditional probability	Probability, conditional probability
25	Probability distribution	Discrete and continuous probability distribution, expected value, variance, standard deviation
26	Term-end examination

Advanced

– The advanced level is designed to provide students with enough mathematical knowledge and maturity to study the IUT mathematics courses.

– In an early stage of the advanced level, the students will go over matrices which are also treated in the intermediate level but their relation with linear transformations are emphasized.

– Then, the program introduces single variable calculus involving more complicated functions than the previous levels.

– This level also provides vector treatment of space geometry. Note also that the language of instruction in the advanced level is English.

№	Subject	Contents
1	Matrices and linear equations	Matrix, sum and product of matrices, determinant, inverse matrix, use of matrices to solve system of 2 linear equations with 2 variables
2	Matrices and linear transformation	Linear transformation and its associated matrices, rotation, reflection about x and y axis
3	Composition of linear transformations and inverse transformation	Composition of linear transformations and inverse transformation and their associated matrices
4	Mathematical induction and sequence of numbers	How to prove a theorem using a mathematical induction, sequences, arithmetic and geometric progressions
5	Limits of sequences and infinite series	Intuitive introduction to limit of a sequence, infinite series, geometric series
6	Trigonometric functions and equations	Manipulation of trigonometric functions using various formulas, inverse trigonometric functions, equations involving trigonometric functions
7	Limits of a function	Intuitive understading of limits of a function in terms of shape of the graph of a function, limits of sum, product, quotient of 2 functions
8	Continuous function	Definition of a continuous function, intermediate value theorem, extreme value theorem
9	Derivative and differentiation	Definition of a derivative, differentiation of polynomial functions, sum and product of two functions
10	Differentiation techniques	Differentiation of trigonometric functions, exponential functions
11	More differentiation techniques	Chain rule, differentiation of inverse functions, related rate real-life problems
12	Application of derivative	Concavity, many worked out examples of graph drawing of various functions using its first and second derivative
13	Mid-term examination
14	Anti-derivative (Indefinite integral)	Definition of indefinite integrals and formulas for indefinite integral, integration by parts, integration by substitution
15	Definite integral	Definition of definite integral and fundamental theorem of calculus
16	Integration techniques	Partial fractions, trigonometric substitutions, many worked out examples of integrations
17	Area on a plane and volume of a rotated solid	Computation of area enclosed by curves, volume of a rotated solid
18	Arc length and other applications of integral	Arc length, motion of a particle (position, velocity, acceleration)
19	Some basic differential equations	Introduction to differential equations and how to solve first order ordinary differential equations
20	Basic combinatorics and binomial theorem	Permutations, combinations, binomial theorem
21	Probability, conditional probability	probability, conditional probability
22	Probability distribution	discrete and continuous probability distribution, expected value, variance, standard deviation
23	Euclidean coordinates in 3 dimensional space	Equation of lines, planes and spheres, angle between 2 planes, orthogonal projection onto a plane,
24	Vectors, inner and cross product of two vectors	Vectors, sum of 2 vectors, a scalar product of a vector, angle between 2 vectors, inner and cross product of 2 vectors
25	Equations of lines and planes in 3 dimensional space	Vector equation of lines, planes and spheres, solving 3 dimensional geometry problems
26	Term-end examination

Mathematics

Admissions

Academics

About

Useful Information

Site Map

Other links