A master's thesis is the result of a study of a certain object (system, process, phenomenon, information technology), its characteristics, and properties. The master's thesis should be related to the solution of scientific and applied problems caused by the specifics of applied mathematics.

The content of the dissertation must be devoted to the research topic, achievement of the goal, and solution of the tasks. Any digressions that are not related to the research objectives are not allowed. The content of the dissertation includes:

• formulation of a scientific and applied problem, definition of the object, subject and purpose of the research, analysis of the state of the art of solving the problem based on the materials of domestic and foreign scientific and technical literature and periodicals, justification of the research objectives
• analysis of possible methods and techniques of research, reasonable choice (development) of the research method
• scientific analysis and generalisation of the factual material used in the research process
• presentation of the obtained results and assessment of their theoretical, applied or scientific and methodological significance
• checking the possibilities of practical implementation of the results obtained
• testing of the results and conclusions in the form of reports at scientific conferences (not lower than the faculty level), publications in scientific journals and collections

The master's thesis should be prepared in accordance with the requirements set out on the page "Requirements for documentation" (but see below for templates).

The approximate length of a master's thesis should be 80-120 pages (excluding appendices).

Based on the results of the master's thesis, at least two papers should be published in the form of reports at scientific conferences (not lower than the faculty level), publications in scientific journals and collections.

A master's thesis for a master's degree consists of the following elements:

• a cover sheet of the prescribed form (see below for formatting templates)
• "Assignment for a master's thesis" of the established sample (see below for templates)
• "Abstract" (in Ukrainian)
• "Abstract" (in English)
• "Table of contents"
• "List of symbols, abbreviations and terms"
• "Introduction"
• sections
• "Conclusions"
• "List of references"
• appendices

The cover page should be designed according to the template at the end of this page. At the same time:

• in the column "As a manuscript", you must indicate the UDC of your master's thesis. The list of UDCs can be found here
• in the column "Admitted to defence", you must indicate the year of the thesis defence
• in the "Supervisor" field, you must indicate the position, academic degree, academic rank, surname and initials of the master's thesis supervisor. Information about the positions, academic degrees, academic titles of the department's lecturers can be found on the page "Lecturers"
• below the supervisor, on separate lines, indicate the positions, academic degrees, academic titles, names and initials of the consultants of individual sections of the master's thesis (if any)
• in the field "Consultant on normative control" you must specify the senior lecturer Malchykov V. V.
• in the "Reviewer" field, indicate the position, academic degree, academic rank, surname and initials of the reviewer of the master's thesis.

The "Master's thesis assignment" should be completed according to the formatting template at the end of this page. At the same time:

• in the "APPROVED" column, you must indicate the year of approval of the master's thesis assignment. In the summer session of 2020, you must specify 2020.
• in the first paragraph, indicate the topic of the master's thesis, surname, name, patronymic (in full), academic degree, academic title of the thesis supervisor, as well as the details of the order by which they were approved.
• in the second paragraph, the deadline for submitting the bound thesis to the department should be indicated.
• in the paragraph "Object of research" you need to indicate the object of research (which is a certain system, process, phenomenon, information technology) that gives rise to a problem situation and is selected for research
• in the paragraph "Subject of research" it is necessary to indicate the subject of research, which is certain properties, characteristics of the object, which are directly aimed at research; the subject of research determines the topic of the dissertation
• in the item "List of tasks to be developed", you need to specify the tasks for individual parts of the master's thesis. These tasks should be formulated in the imperative mood, starting with the words "develop", "perform", "analyse", "conduct", etc.
• in the item "Indicative list of illustrative material", the names of the key figures for the master's thesis and the slides of the presentation that the student will make during the master's thesis defence should be indicated
• in the item "Indicative list of publications" it is necessary to indicate the (approximate) titles of the student's publications on the topic of the dissertation in scientific journals, collections of scientific papers, materials, abstracts of scientific conferences, etc.
• in the item "Consultants of the dissertation chapters", the names of the chapters, as well as the names, initials and positions of the consultants of these chapters (if any, otherwise this item can be omitted) should be indicated in separate lines of the table. It is worth noting that the consultant on normative control is a consultant for the entire dissertation, not for individual chapters, so it is not necessary to indicate it in this paragraph
• in the "Date of assignment" item, you need to specify the date on which the student was assigned a master's thesis.

In the "Timeline", the stages of the master's thesis and their deadlines should be presented in tabular form. The "Note" column can be left blank.

The "abstract" is intended to introduce the thesis. It should be concise, informative and contain information that allows you to reveal the essence of the research.

The "abstract" should consist of the following items (see below for templates):

• information on the volume of the master's thesis (WITHOUT appendices), the number of figures, tables, appendices and bibliographic references in the "List of References"
• "Relevance of the topic": disclosure of the essence and state of the scientific and applied problem, its relevance and significance, justification of the feasibility of the study
• "Relationship of the work to scientific programmes, plans, topics": in this paragraph, it is sufficient to state the following: "The dissertation was carried out in accordance with the plan of research work of the Department of Applied Mathematics of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"."
• "Purpose and objectives of the study": the purpose of the study and the tasks to be solved to achieve it. The goal is the planned result of the research. The purpose of any scientific work is to identify new facts, conclusions, recommendations, patterns, and clarify previously known but insufficiently researched facts. Research tasks are formulated as independently completed research stages or as a sequential solution to individual research questions in relation to the entire master's thesis. The research objectives should be drawn up in the form of an unnumbered list
• "Object of research": this item must fully correspond to the item "Object of research" from the "Tasks for master's thesis"
• "Subject of research": this item must fully correspond to the item "Subject of research" from the "Task for master's thesis"
• "Research methods": a list of research methods used to achieve the goal set in the dissertation. The methods must be presented with an indication of why they were used
• "Scientific novelty of the results obtained": a brief summary of the new achievements that the student has obtained independently. It is necessary to note the difference between the results obtained and those known earlier. The statement of scientific novelty should be made in the form of an unnumbered list, each item of which should have the following approximate structure: "for the first time/improved/further developed [...], which differs from the existing ones in that [...], which made it possible [...]"
• "Practical significance of the results obtained": information on the application of research results or recommendations for their implementation (use). If relevant materials are available, brief information on the implementation of research results should be provided, indicating the names of organisations and details of relevant documents
• "Approval of the dissertation results": information about the student's presentations at scientific conferences, seminars, etc. on the topic of the dissertation
• "Publications": information about the student's publications on the topic of the dissertation in scientific journals, collections of scientific papers, materials, abstracts of scientific conferences, etc. (only the total number of publications should be indicated, as well as the number of works by category, separately indicating the number of individual works in each category)
  keywords (from 5 to 15 positions)

"Abstract" should be a translation of the abstract into Ukrainian. The titles of the abstract's paragraphs must also have this translation:

• "Topic Relevance" - "Topic Relevance"
• "Thesis connection to scientific programmes, plans, and topics" (in this paragraph, it is sufficient to state the following: "The thesis was prepared in accordance with the scientific research plan of the Applied Mathematics Department of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute.")
• "Research goal and objectives" - "Research goal and objectives"
• "Object of research" - "Object of research"
• "Subject of research" - "Subject of research"
• "Methods of research" - "Methods of research"
• "Scientific novelty of the results obtained" - "Scientific contribution"
• "Practical value of obtained results" - "Practical value of obtained results"
• "Approbation of the thesis results" - "Approbation of the thesis results"
• "Publications" - "Publications"

"The Introduction should contain a literature review that reveals the state of the scientific and applied problem and its significance. It should indicate the issues that remain unresolved and determine the place of the dissertation in solving the relevant problem.

In the chapters of the master's thesis, you need to submit

• review of existing theoretical and practical solutions on the topic of the dissertation, their comparative analysis
• description of a new or improved mathematical model, method(s) for solving the problem
• description of software tools for solving the problem, including developed algorithms. In a master's thesis, it is not necessary to describe the graphical user interface, user manual and other characteristics of software tools that are not relevant to the research
• description of the testing of software tools that implement the mathematical models and methods developed/improved in the thesis

If the master's thesis has a pronounced engineering character, one of its sections may be devoted to the development of a start-up. The structure of such a chapter must comply with the current regulations of Igor Sikorsky Kyiv Polytechnic Institute.

Each chapter of the work should end with the subsection "Conclusions to the chapter".

In the Conclusions, the most important scientific and practical results obtained in the dissertation should be stated, the qualitative and quantitative indicators of the relevant results, conclusions and recommendations for the scientific and practical use of the results should be indicated.

The "Conclusions" should be drawn up in the form of a numbered list, the number of items in which, as a rule, corresponds to the number of research objectives set out in the "Abstract".

The "List of References" should be drawn up in accordance with the requirements for the "List of References" on the page "Requirements for Documentation".

The "List of References" must contain references to the student's own works, which, in turn, must be referenced in the text of the dissertation.

The following are NOT allowed in the "List of References":

• references to sources that have no scientific value
• links to Wikipedia pages and similar resources that do not have a scientific review process
• sites of abstracts and other document storage that have no scientific value
• course and laboratory works
• file sharing sites (and other similar resources)

Instead of linking to a file with a scanned source, you must provide a description of the printed publication!

Based on the results of the master's thesis, at least two papers should be published in the form of reports at scientific conferences (not lower than the faculty level), publications in scientific journals and collections.

The master's thesis must contain the following mandatory appendices, among others:

• the first appendix should be the appendix "Program Listings", which should include listings of the program code for the implementation of the mathematical models, methods and algorithms described in the thesis. The code of the graphical user interface may not be listed. At least 30% of the listing lines should be comments. The volume of listings should be 15-40 pages. It is worth remembering that the length of the listings does not affect the length of the master's thesis!
• the penultimate appendix should be the "Illustrative Material" appendix, which should include the slides of the presentation that the student will make during the master's thesis defence
• the last appendix, if there are relevant materials, should be the appendix "Certificates of implementation of the dissertation results", which should include scanned copies of certificates (acts) on the implementation of the results of the master's dissertation. In the absence of such materials, this appendix may be omitted

The Department of Applied Mathematics has prepared design templates that take into account the above requirements, as well as the requirements for the design of title pages and master's thesis assignments. The current version of these templates is provided to students during their pre-diploma practice.