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 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

  • 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

 

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.

 

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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.  

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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.

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