Information as one of the main all-encompassing terms in modern science. Information transfer in various types of systems. The role of information and related processes in the world around us.
Data is information in a formalized form that is suitable for storage, transfer, and processing. Information processes are processes related to data storage, conversion, and transfer.
Data representation. Data for storage and processing in automated computer systems VS data intended for human perception: differences in representation.
Systems. System components and their interaction. Character, sign, signal. Information interaction in the system. Open-loop and closed-loop control systems. Mathematical and computer modeling of control systems.
Uniform and non-uniform codes. Prefix codes. Fano сondition. Reverse Fano condition. Decoding algorithms with prefix codes.
Examples of codes used for encoding texts: ASCII, UNICODE standard. Encoding Cyrillic and other national alphabets; code pages.
Data compression. Frequency of characters with non-uniform codes. Optimal Huffman encoding. Use of programs-archivers. The LZW algorithm.
Data transfer. Source, receiver, communication channel, signal, encoding and decoding device.
Bandwidth and noise immunity of the communication channel. Encoding of messages in modern data transferring media.
Distortion of information in communication channels. Codes with the ability to detect and fix errors.
Methods for protecting information transferred through communication channels. Cryptography (encryption algorithms). Steganography.
Basic school topics to revise:
Alphabet, text, length of text. The number of different texts of a given length in a given alphabet. Encoding characters in one alphabet using code words in another alphabet; code table, decoding.
Measurements and discretization. Frequency and bit depth of measurements. The versatility of discrete representations of information.
Discrete representation of audio data. Multichannel recording. The size of the file obtained as a result of audio recording.
Discrete representation of graphical information. Color model. RGB and CMYK models. HSB and CMY models. Depth of coding.
Compression of data when storing graphic and audio information.
Properties of positional notation: the number of digits, divisibility rule (whether a number is divisible by the base of the numeral system).
Algorithm for converting decimal notation to notation a positional system with a given base. Algorithms of number notation in a positional numeral system with a given base, algorithms of calculating a number according to a line containing this number in a positional numeral system with a given base.
Arithmetic operations in positional numeral systems.
Short and expanded form of writing mixed numbers in positional notation. Converting a mixed number to positional numeral system with a given base.
Representation of integers and real numbers in computer memory. Computer arithmetic.
Basic school topics to revise:
ositional numeral systems. Expansion of a number by degrees of the base of the numeral system. Binary notation.
Octal notation. Triads of the octal system. An algorithm for converting from binary to octal and back again. Hexadecimal notation. Tetrads of the hexadecimal system. An algorithm for converting from binary to hexadecimal and back.
Operations "implication" and "equality". Logic functions.
Rules of logic algebra. Equivalent transformations of logical expressions. Logical equations.
Building a logical expression with given truth table. Disjunctive normal form. Conjunctival normal form.
Logical elements of computers. Building schemas from basic logic elements. Trigger. Adder.
Discrete two-player games with complete information. Winning strategy.
Basic school topics to revise:
Calculation of the number of options: formulas for multiplying and adding the number of options. Logical operators. Logical operators NOT, AND, OR. Tables of truth of logical expressions of a set and operations with them. Euler-Venn diagrams.
Directed and undirected graphs; cycle and acyclic graphs; starting vertice (source) and ending vertice (drain) in a directed acyclic graph; distance between vertices.
Algorithmic problems related to graph analysis (examples: the problem of constructing an optimal path between vertices of a directed acyclic graph; the problem of determining the number of different paths between vertices).
Trees. Subtrees; traversal of the tree in depth. Ordered trees (trees that have ordered edges that come out of a single node).
Use of trees in solving algorithmic problems (examples: analysis of recursive algorithms, analysis of arithmetic and logic expressions).
Using graphs, trees, and lists to describe objects and processes in the world around us.
Basic school topics to revise:
List. First element, last element, previous element, next element. Insert, delete, and replace an element.
Graph. Vertex, edge, path. Directed and undirected graphs. Length (weight) of the edge and path. The concept of a minimal path. The adjacency matrix of the graph (0/1 matrix) and the weight matrix (specifying edge lengths).
Tree. Root, leaf, vertex (node). Previous vertex, the next vertices. Subtrees. Tree height. Binary tree.
The algorithms for studying a square equation with integer and real coefficients.
The algorithms for analyzing and converting number notations in the positional numeral system.
The algorithms associated with the divisibility of integers. Euclid's algorithm for finding the greatest common divisor of two natural numbers.
The algorithms for linear (single-pass) processing of a sequence of numbers without using additional memory that depends on the sequence length (calculating the maximum, sum, linear search, etc.). Processing of sequence elements that meet a certain condition (calculating the sum of such elements, their maximum, etc.).
Recursive algorithms. Notating them without using recursion. Сalculation of the elements of a recursive sequence. The construction and analysis of the tree of recursive calls.
Algorithms for processing arrays. Inserting and deleting elements in the array.
Sorting one-dimensional arrays. Quadratic sorting algorithms (example: bubble sorting). Merging two sorted arrays into a single array without using sorting. Recursive implementation of sorting by merging two sorted sub-arrays.
Calculating the value of a polynomial of a given degree at a given point (the values of the coefficients of the polynomial are set by an array).
Algorithms for analyzing strings.
Graphing a function defined by a formula, program, or table of values.
Algorithms for approximate solution of equations. Algorithms for approximate calculation of lengths and areas. Approximate calculation of the figure area using the Monte Carlo method. Building trajectories set by differential schemes. Tackling optimization problems. Algorithms for computational geometry. The probabilistic algorithms.
Saving and using intermediate results. Dynamic programming method.
Data structures: lists, dictionaries, trees, and queues. Hash tables.
Subroutines (procedures, functions). Parameters of subroutines. Recursive procedures and functions.
Logic variables. Character and string variables. String operations.
Two-dimensional arrays (matrices). Multidimensional arrays.
Tools for working with data in external memory. Files.
Detailed introduction to one of the universal procedural programming languages. Notation of algorithmic constructions and data structures in the selected programming language. Overview of procedural programming languages.
The concept of non-procedural programming languages and programming paradigms. Learning a second programming language.
Basic school topics to revise:
The main algorithmic constructions: "following" (sequential execution of commands)," branching" and "loop". Table values (arrays). One-dimensional arrays. Two-dimensional arrays.
Encoding of basic algorithmic structures in the selected programming language. Assignment operator. Constants and variables. Variable: name and value. Types of variables: integer and real ones.
Stages of solving problems on the computer.
Structural programming. Checking the loop condition before executing the loop body and after executing the loop body: the postcondition and precondition of the loop. The loop invariant.
Top-down and bottom-up program design. Development of programs that use subroutines.
Subroutine libraries and their use.
The concept of object-oriented programming. Objects and classes. Encapsulation, inheritance, polymorphism.
Fast software development environments. Graphical design of the user interface. Using modules (components) in programming.
Basic school topics to revise:
Checking the health of the program using trace tables.
Formalization of the algorithm concept. The Turing machine is an example of an abstract universal computational model. The Church – Turing Thesis.
Other universal computing models (example: the Post machine). Universal algorithm. Computable and uncomputable functions. The stopping problem and its unsolvability.
Abstract universal generative models (example: grammars).
Calculation complexity: the number of operations performed, memory used, and their dependence on the size of the source data.
Complexity of the merge sorting algorithm (MergeSort).
Examples of algorithm analysis tasks: determining the input data for which the algorithm gives the specified result; finding the result of the algorithm without its full step-by-step execution.
The proof of the correctness of programs.
Basic school topics to revise:
Server. The need for a formal description of the server. Algorithm as a plan for managing the server(s).
Practical work with a computer model on the selected topic. Conducting a computational experiment. Analysing reliability (plausibility) of experimental results.
Representation of modeling results in a form that is convenient for human perception. Graphical representation of data (diagrams, tables, graphs).
Building mathematical models for solving practical problems.
Simulation modeling. Modeling of queuing systems.
Discretization and numerical methods in mathematical modeling of continuous processes.
Use of simulation environments (virtual laboratories) for conducting computer experiments in education.
Use of educational computer-aided design systems.
Basic school topics to revise:
Concept of a mathematical model. Problems solved using mathematical (computer) modeling.
Modeling cycle: building a mathematical model, its software implementation, checking the model's compliance with the object or process of modeling using simple examples (testing), conducting a computer experiment, analyzing its results, refining the model
Computer hardware. Personal computer.
Multiprocessor systems. Supercomputers. Distributed computing systems and big data processing. Mobile digital devices and their role in communications. Embedded computer. Microcontrollers. Automatic production.
Adequacy of the computer configuration to the tasks being solved. Trends in computer hardware development.
Software for computers and computer systems. Various types of software and their purpose: system software (operating systems, embedded software, programming systems), application software (word processors, browsers, etc.). software for mobile devices.
Installing and uninstalling software. System administration.
Computer viruses and malware. The use of antivirus tools.
Preventive maintenance of computer hardware and software.
Legal rules for using computer programs and working online. Legislation of the Russian Federation concerning software.
Precautions and rules for working on the computer. Hygiene, ergonomics, resource saving, technological requirements at a computer workplace. Designing an automated workplace in accordance with the purposes of its use.
Creating text documents. Inserting graphic objects and tables. Use of pre-made templates and making your own templates.
Search and replace tools. Spell and grammar checking. Pagination. Inserting footnotes and links, document structure mode, making a hypertext document. Bibliographic description of documents. Collective work with documents.
Tools for entering text. OCR. Speech recognition. Computer text layout. Desktop publishing capabilities.
Tools for creating and editing mathematical texts.
Technical means for entering graphic images. Cropping images. Color model. Image correction. Working with multi-layer images.
Working with vector graphic objects. Grouping and transforming objects.
Technologies for entering and processing audio and video information.
Image, audio, and video file formats.
Multimedia presentations. Making animation, animation adjustment.
Computer 3D modeling. Computer-aided design systems.
Processing technology for numerical information. Entering and editing data. Autocomplete. Cell formatting. Standard functions. Types of links in formulas. Solving computational problems from various areas.
Computer-based data representation and analysis. Data visualization.
Technology of carrying out a research project: setting a task, selecting research methods, drafting a project and work plan, preparing initial data, conducting research, making conclusions, making a report. Verification (verification of reliability and consistency) of initial data and validation (verification of validity) of research results.
Statistical data processing. Processing of the results of the experiment.
Data analysis using machine learning methods. Big data.
Concept and purpose of a database (DB). Types of database. Database management systems (DBMS). Tables. Record and field. Key field. Data type. Request. Types of query. Queries with parameters. Sorting. Filtration. Calculated field.
Multi-table databases. Links between tables. Normalization.
The Internet. Domain names system. Internet Services. WWW technology. Cloud services. Internet protocols. IP addresses and subnet masks.
Search engines in computer networks. Rules for making queries.
Personal information space of a user. Network community. Publication of materials on the Internet. Use of information systems on the Internet. Ecommerce.
Making web sites. HTML language, cascading style sheets (CSS). Dynamic HTML. Hosting websites.
Standards in Informatics and ICT. State electronic services and services. Mobile application. Open educational resources. Information culture.
Rules of behavior and information security online. Electronic digital signature. Netiquette.
Legal support of information security of the Russian Federation. Information security tools in computers, automated information systems, and computer networks.
Applicants to MIPT are expected to know the basic theoretical principles of chemistry, the methods of preparing redox reactions, the main classes of inorganic and organic compounds, mathematical tools to describe chemical processes from the quantitative side, the basic concepts and laws of chemistry, they should also be able to characterize chemical compounds in terms of their acid-base and redox properties. The characteristics of each class of organic compounds contain the features of the electronic and spatial structure of compounds of this class, the patterns of changes in physical and chemical properties in the homologous series, the nomenclature, types of isomerism, the main types of chemical reactions and their mechanisms.
The written part of the entrance test includes theoretical tasks on the topics The structure of the atom and Chemical bonds. It also includes combined computational problems based on various sections of chemistry. Besides, it includes chains of transformations and reaction equations in inorganic and organic chemistry.
Goal and objectives of chemistry. The place of chemistry in natural sciences. Physical and chemical phenomena. Basic concepts of chemistry.
Law of stoichometry (Avogadro's law, Proust's Law of Constant Proportion, Law of Conservation of Mass, Gay-Lussac's Law of Gaseous Volumes, Law of Multiple Proportions) Atomic Molecular Theory. Constitution of atom. Isotopes. Structure of atomic electron shells. Electron configuration.
Mendeleev’s Periodical law and it’s support by the electronic structure of atoms. Periodic table of elements. Periodicity of atomic properties.
Chemical bond and its properties. Electronegativity. Types of chemical bonds.
Aggregation states of matter. Classification and nomenclature of chemical compounds. Main classes of inorganic compounds: oxides, hydroxides, salts. Synthesis and properties of oxides, hydroxides and salts
Chemical reactions and their classification.
Rate of chemical reactions. Law of mass action. Factors that affect rate of a chemical reaction. Catalysis and catalysts. Reversible and irreversible reactions. Chemical equilibrium. Shifting of chemical equilibrium. Le Chatelier's principle (equilibrium law)
Solutions. The different ways to represent concentrations in solution. Electrolytes. Solutions of electrolytes. Exchange reactions in solutions of electrolytes. Hydrolysis of salts. Ionic equilibrium between solution and solid state.
Redox reactions in solutions. Determination of stoichiometric coefficients in redox reactions. Electrolysis of electrolytes solutions and melts . Applications of electrolysis.
Halogens. General characteristic of chemical properties of halogens on the basis of their location in the Mendeleev’s periodic table of elements. Hydrochloric acids and its salts. Oxygen-containing acids of chlorine and their salts.
General characteristic of chemical properties of main group VI Mendeleev’s periodic table of elements. Oxygen. Allotropy of oxygen. Sulfur. Physical and chemical properties of Sulfur. Hydrogen sulfide. Sulfur dioxide and trioxide. Sulfuric acid. Sulfates. Sulfurous acid and its salts.
General characteristic of chemical properties of main group V of Mendeleev’s periodic table of elements. Nitogen. Ammonia. Industrial production of ammonia. Physical and chemical properties of ammonia. Ammonium salts. Nitric acid. Chemical properties of nitric acids. Salts of nitric acid. Nitrous acid and its salts. Phosphorous. Allotropes of phosphorus. Phosphoric acid and its salts.
General characteristic of chemical properties of main group IV elements of Mendeleev’s periodic table of elements. Carbon. Allotropes of carbon. Physical and chemical properties of carbon. Carbon (II) and carbon (IV) oxides and their salts. Carbonic acid and its salts.
Alkali and alkaline metals. General properties of alkali metals based on its location in the Mendeleev’s periodic table of elements. Calcium. Water hardness and ways to remove it.
Aluminium. General properties of aluminium based on its location in the Mendeleev’s periodic table of elements. Production, physical and chemical properties of aluminium. Amphoteric properties of aluminium oxide and aluminium hydroxide.
Iron. Physical and chemical properties of iron. Oxides and hydroxides of iron (II) and (III). Dependence of chemical properties of iron compounds on oxidation state of iron.
Selected fourth period d-elements of Mendeleev’s periodic table of elements (chromium, manganese, copper, zinc). Interactions of zinc and chromium with acid and bases. Copper reaction with acids. Reactions of zinc and chromium hydroxides with bases and acids. Common oxidation states of chromium and manganese in their compounds. Chemical properties of fourth period d-block elements compounds.
The key points of the Butlerov’s theory of chemical structure of organic compounds.
Classification of organic compounds based on structure: acyclic (alkanes, alkenes, alkynes, alkadienes), carbocyclic (cycloalkanes, arenes) and heterocyclic. Classification of organic compounds based on functional groups. Homologous series in organic compounds.
Chemical reactions in organic chemistry. Classification of organic reactions based on the mechanism of bond cleavage.
Chemical properties of alkanes. Halogenation reactions. Nitration of alkanes. Sulfochlorination. Combustion of alkanes at different conditions (Oxidation reactions). Dehydrogenation. Isomerisation and cracking.
Chemical properties of cycloalkanes: combustion, decomposition, radical substitution, isomerisation. Unique properties of cyclopropane and cyclobutane.
Chemical properties of alkenes: addition and oxidation reactions.
Chemical properties of alkadienes: electrophilic addition. Reaction of polymerization – production of synthetic rubber.
Chemical properties of alkynes. Trimerisation of acetylene to benzene. Oxidation reactions of alkynes.
Benzene as a typical arene. Homologs of benzene. Substitution reaction of benzene: halogenation, nitration, alkylation. Application of benzene and homologs.
Chemical nomenclature and classification of alcohols. Phenols. Chemical properties of hydroxy compounds. Reactions involving the O-H bond of alcohols: substitution of hydrogen by metal, substitution of hydrogen by carboxyl group (ester formation), removal of hydrogen by oxidation or dehydration. Oxidation of alcohols. Reactions involving the C-O bond of alcohols: substitution of hydroxyl group by nucleophiles, intermolecular dehydration, intramolecular dehydration (ether formation). Chemical properties of phenol (substitution in the aromatic ring): nitration, halogenation, condensation with aldehydes.
Chemical nomenclature of aldehydes and ketones. Typical reactions of carbonyl compounds: Addition to carbonyl groups, polymerization, condensation, reduction and oxidation.
Chemical nomenclature and classification of carboxylic acids. Isomerism of carboxylic acids. Electronic structure of carboxyl group. Chemical properties of carboxylic acids derivatives.
Chemical nomenclature and classification of amines. Isomerism of amines. Basicity of amines. Aromatic amines. Chemical properties of amines. Combustion of amines.
Amino acids. Chemical composition and structure of amino acids. Reaction of amino acids with bases. Reaction of amino acids with acids. Synthesis of amino acids esters.
Peptides as natural biopolymers. Peptide functional group and peptide bond. Chemical reactions representing interconnections of various classes of organic compounds (Interconversions of classes).
Biology exam requires: