Mathematics
Mathematics
1. The IUT preuniversity mathematics curriculum offers its students chances to study mathematics more thoroughly and systematically, supplementing their high school class work.
2. The preuniversity courses in mathematics are designed to help students to understand fundamental concepts and work out more challenging problems.
3. The IUT preuniversity mathematics program offers three levels of curriculum depending on the students’ mathematical knowledge and problemsolving 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 2x2 matrix, Use of matrices to solve system of 2 linear equations with 2 variables 
4 
Exponents 
Manipulation of exponents and nth 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 
Midterm 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 
Antiderivative (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 
Termend 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 2x2 matrix, Use of matrices to solve system of 2 linear equations with 2 variables 
4 
Exponents and exponential functions 
Manipulation of exponents and nth 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 
Midterm 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 
Antiderivative (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 
Termend 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 reallife problems 
12 
Application of derivative 
Concavity, many worked out examples of graph drawing of various functions using its first and second derivative 
13 
Midterm examination 

14 
Antiderivative (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 
Termend examination 
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