Courses
1. 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 
2. Physics
1. The IUT preuniversity curriculum in Physics includes all of the highschool physics courses and some basic university physics courses.
2. The preuniversity courses in physics intend to help students well prepare to learn and understand university physics at IUT.
3. There are three kinds of curriculum according to the level of courses: Basic, Intermediate, and Advanced Level.
4. The scope of each level is described as in the following.
 Basic Level
 The basic level is an introduction to physical worlds for high school students who have learned the physics subject for less than 1 year or even haven't learned physics at all.
 This level provides basic concept on physical phenomena with only a little mathematical treatment.
№ 
Subject 
Contents 
1 
Measurement 
Measuring things, Standards and units, International system of units 
2 
Straight line motion 1 
Position and speed, Motion with constant velocity 
3 
Straight line motion 2 
Acceleration, Motion with constant acceleration, Freelyfalling bodies 
4 
Newton's laws of motion 1 
Newton's first law, Force, Newton's second law, Mass and weight 
5 
Newton's laws of motion 2 
Newton's third law, Applying Newton's laws in straight line motion 
6 
Work and Energy 1 
Work, Work done by the gravitational force and a spring force 
7 
Work and Energy 2 
Kinetic energy, Workenergy theorem, Power 
8 
Momentum and Impulse 
Linear momentum, Collision and impulse, Momentumimpulse theorem 
9 
Conservation of momentum 
Conservation of momentum in collision along a straight line 
10 
Periodic motion 
Describing oscillation, Simple harmonic motion, Energy in simple harmonic motion 
11 
Temperature and Heat 
Measuring temperature, Kelvin scale, Quantity of heat, Heat and energy 
12 
Thermal expansion and Heat transfer 
Thermal expansion, Heat transfer (Conduction, Convection, Radiation) 
13 
Midterm examination 

14 
Electric charge and Coulomb's law 
Electric charge, Conductors and insulators, Electric force and Coulomb's law 
15 
Electric field 
Electric field by a point charge, Electric field lines 
16 
Ohm's law 
Electric current, Voltage, Resistance, Ohm's law 
17 
Electric circuit 1 
Resistors in series and parallel, Singleloop circuit 
18 
Electric circuit 2 
Multiloop circuits, Kirchhoff's rules, Energy and power in electric circuits 
19 
Capacitor 1 
Parallelplate capacitor, Capacitance, Capacitors in series and parallel 
20 
Capacitor 2 
Electricfield energy, Energy storage in capacitors, Dielectrics 
21 
Waves 
Periodic waves, Wavelength and frequency, Types of waves 
22 
Propagation of light 1 
Electromagnetic wave spectrum and light, Reflection and refraction, Index of refraction, Snell's law 
23 
Propagation of light 2 
Total internal refraction, polarization 
24 
Geometric optics 1 
Two types of images, Plane mirrors, Spherical mirrors 
25 
Geometric optics 2 
Thin lenses, Optical instruments (eye, camera, magnifier) 
26 
Termend examination 
 Intermediate
 The purpose of the intermediate level is to help students develop and understand the physical world at a deep and fundamental level.
 This level is appropriate for those high school students who have learned the physics subject for about 1 year and equipped themselves with some mathematical skills.
№ 
Subject 
Contents 
1 
Vector quantities 
Vectors and scalars, Components of vectors, Products of vectors 
2 
Motion in two or three dimensions 
Displacement, velocity, and acceleration vectors in a plane, Relative velocity 
3 
Projectile and Circular motion 
Projectile motion, Uniform circular motion 
4 
Newton's laws of motion 
Applying Newton's laws of motion in two dimensions 
5 
Friction and Centripetal force 
Properties of friction, Drag force and terminal speed, Circular motion and centripetal force 
6 
Conservation of energy 
Work and potential energy, Conservation of mechanical energy 
7 
Momentum and Collision 1 
Momentum and kinetic energy in collision, Elastic and inelastic collision 
8 
Momentum and Collision 2 
Collision and momentum conservation in twodimensions 
9 
Gravitation 1 
Newton's law of gravitation, Gravitation near Earth's surface 
10 
Gravitation 2 
Gravitational potential energy, Kepler's laws and motion of planets 
11 
First law of thermodynamics 
Thermodynamic systems, Heat, work, and internal energy in thermodynamic systems, The first law of thermodynamics 
12 
Thermodymic processes 
Kinds of thermodynamic processes, Some special cases of the first low of thermodynamics 
13 
Midterm examination 

14 
Electric field and Potential 
Electric field by electric charges, Electric potential and Emf, Dielectrics and conductors 
15 
RC circuit 
Electric circuits with resistors and capacitors, The RC circuit 
16 
Magnetic field 
Magnetic field, Motion of charged particles in a magnetic field 
17 
Magnetic field and Current 1 
Magnetic field of a moving charge and current, Law of Biot and Savart 
18 
Magnetic field and Current 2 
Ampere's law, Force between parallel currents, Magnetic field in solenoids and toroids 
19 
Electromagnetic induction 
Faraday's law of induction, Lenz's law, Induced electric field 
20 
Transverse waves 
Mathematical description of waves, Principle of superposition, interference of waves, standing waves 
21 
Longitudinal waves and Sound 
Sound waves, Musical sound, Interference and beat, Decibel level, Doppler effect 
22 
Interference of light 
Light as a wave, Young's doubleslit experiment, Interference in thin films, Michelson interferometer 
23 
Diffraction of light 
Huygens's principle, Diffraction by a slit, Diffraction grating and a spectrometer 
24 
Particle nature of light 
Blackbody radiation, Photoelectric effect, Compton's experiment 
25 
Light quanta and Matter waves 
The duality of light, Light as a probability wave, Electrons and matter waves, Heisenberg's uncertainty principle 
26 
Termend examination 
 Advanced
 The advanced level includes some topics in the university physics along with advanced topics in high school physics.
 This level is appropriate for those high school students who have learned the physics subject for about 2 years and have good ability of mathematical skills.
№ 
Subject 
Contents 
1 
Conservation of energy 
Conservative forces and path independence, Conservation of mechanical energy and total energy 
2 
Momentum and Collision 
Center of mass, Momentum of a system of particles, Momentum conservation in rocket propulsion 
3 
Gravitation 
Motion of Satellites, Escape velocity, Black holes 
4 
Rotational motion 
Rigid body, Angular velocity and acceleration, Moment of inertia 
5 
Rotational motion and Angular momentum 
Kinetic energy of rotation, Torque, angular momentum, Conservation of angular momentum 
6 
Equilibrium and Elasticity 
Equilibrium, Conditions for equilibrium, Elasticity, Stress and strain 
7 
Fluid mechanics 1 
Density and pressure in a fluid, Pascal's principle 
8 
Fluid mechanics 2 
Buoyancy, Fluid flow and Bernoulli's equation 
9 
Simple harmonic motion 
Simple harmonic motion in a simple pendulum, The physical pendulum 
10 
Kinetic theory of ideal gases 
Equation of state, Kinetic energy of ideal gases, Distribution of moelcular speeds, Degree of freedom 
11 
Second law of thermodynamics 
Irreversible processes and entropy, Change in entropy, The second law of thermodynamics 
12 
Heat engines 
Heat engines and refrigerators, Efficiency of real engines, The Carnot cycle 
13 
Midterm examination 

14 
Gauss' law and electric field 1 
Flux of electric field, Gauss' law, Gauss' law and Coulomb's law 
15 
Gauss' law and electric field 2 
Application of Gauss' law in symmetric systems, Gauss' law in capacitors 
16 
Inductors and Inductance 
Selfinductance and inductors, Magneticfield energy in inductors, Mutual inductance 
17 
RL circuit 
Electric circuit with resistors and inductors, The RL circuit 
18 
Alternating current 
Alternating current, RLC series circuit, Reactance and impedance 
19 
Power in AC circuits and Transformers 
Power in AC circuits, Transformers, Electric power transmission 
20 
Maxwell's equation and Electromagnetic waves 
Gauss's law for magnetic field, Displacement current, Maxwell's equations, Electromagnetic waves and speed of light 
21 
Relativity 1 
Einstein's postulates, Special theory of relativity, The relativity of simultaneity, time, and lentgth 
22 
Relativity 2 
Relativistic momentum and kinetic energy, The general theory of relativity 
23 
The model of an atom 
Rutherford's model of an atom, Hydrogen spectrum, The Bohr model of Hydrogen 
24 
Nuclear physics 
Nucleon, Isotope, Radioactivity, Radioactive decay, Halflife, Nuclear reaction, Nuclear fission and fusion 
25 
Fundamental particles and Cosmology 
Leptons and hadrons, The Quark model, The basic forces, The big bang and cosmic background radiation, Dark matter 
26 
Termend examination 
3. English
There are two programs at English: General English and IELTS.
The program of General English is below:
 Speaking and Listening: Help prospective students develop English skills needed to be communicatively competent in the era of globalization.
 Grammar and Reading: Encourage prospective students to be academically well prepared for study in college or university.
Note: This program is for Basic Level Group.
The program of IELTS is below:
 Listening Test
 Academic Reading Test
 General Training Reading Test
 Academic Writing Test
 General Training Writing Test
 Speaking Test
Note: This program is for Advanced and Intermediate Level Group.
Additional information: English native speaker teaches pronunciation and English conversation at all groups 3 hours per a week
 Basic Level
 Helping students in improving English ability
 Intermediate Level
 Helping students in receiving 5 degree of IELTS
 Advanced Level
 Helping students in receiving 5 more degree of IELTS
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