## Courses

1. 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 2x2 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 2x2 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

- 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

2. Physics

1. The IUT pre-university curriculum in Physics includes all of the high-school physics courses and some basic university physics courses.

2. The pre-university 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, Freely-falling 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, Work-energy theorem, Power 8 Momentum and Impulse Linear momentum, Collision and impulse, Momentum-impulse 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, Single-loop circuit 18 Electric circuit 2 Multi-loop circuits, Kirchhoff's rules, Energy and power in electric circuits 19 Capacitor 1 Parallel-plate capacitor, Capacitance, Capacitors in series and parallel 20 Capacitor 2 Electric-field 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 Term-end 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 two-dimensions 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 Mid-term 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 double-slit 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 Term-end examination

- 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 Mid-term 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 Self-inductance and inductors, Magnetic-field 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, Half-life, 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 Term-end 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
• 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
• Helping students in receiving 5 more degree of IELTS

## IN FOCUS

#### Benefits for Pre-University students

Inha University in Tashkent provides following benefits to the students of the Pre-University courses:

• Students will be exempted from taking the IUT entrance examination if they get 60 points for each subject during the final examination.
• Only Pre-University students have a second chance to take the entrance examination.
• First and second year students of colleges and academic lyceums will become the IUT students after a successful completion of their studies.
• Pre-University students have an opportunity to use the university facilities.

## Why IUT?

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#### Why should I study at IUT?

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#### Why should I choose IUT?

It has been over 60 years since Inha University was established upon the ideals of leadership and expertise and service to the country.

#### Mission and objectives of the Inha University in Tashkent (IUT)

The central mission of Inha University in Tashkent is to achieve excellence in the undergraduate and graduate education. Apply for

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