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7.3. Tables, formulas, drawings, figures, diagrams and charts in academic work

Lecture



A table is a way of presenting information in which numerical or textual material is grouped into columns separated from one another by vertical and horizontal rules.

By content, tables are divided into analytical and non-analytical ones. Analytical tables are the result of processing and analysing numerical indicators. As a rule, after such tables a generalization is made as new (inferred) knowledge, which is introduced into the text with the words: "the table allows us to conclude that...", "it is clear from the table that...", "the table makes it possible to conclude that..." etc. Such tables often make it possible to reveal and formulate certain regularities. Non-analytical tables generally contain unprocessed statistical data, needed only for information or statement of fact.

The heading of each column in the table head should be as precise, simple and, where possible, brief as possible. Repetitions of the thematic heading in the column headings should be eliminated; a tier indicating the unit of measurement should be removed, transferring it to the thematic heading; recurring words should be moved into combining headings.

All tables, if there are several, are numbered with Arabic numerals throughout the whole text. Above the top right-hand corner of the table the inscription "Table..." is placed, indicating the serial number of the table (for example "Table 4"), without the No. sign before the figure and without a full stop after it. If there is only one table in the text of a scholarly work, no number is assigned to it and the word "table" is not written. Tables are provided with thematic headings, which are placed in the middle of the page and written with a capital letter, without a full stop at the end.

When a table is carried over to the next page, the table head should be repeated and above it the words "Continued from Table 5". should be placed. If the head is cumbersome, it is permissible not to repeat it. In this case the columns are numbered and their numbering is repeated on the next page. The table heading is not repeated.

All data given in tables must be reliable, homogeneous and comparable, and their grouping must be based on essential characteristics.

Only those tables that are difficult to convey in ordinary text (results of experimental observations, comparison of divergence, detailed reference information, etc.) should be included in a scholarly work.

Let us consider the general procedure for presenting formulas, so as to bring their formatting as close as possible to publishing requirements.

The most important formulas, as well as long and cumbersome formulas containing summation, product, differentiation, and integration signs, are placed on separate lines. All numbered formulas are placed in the same way.

Only the most important formulas, which are referred to in the subsequent text, should be numbered. It is not recommended to number formulas that are not referred to in the text.

The serial numbers of formulas are indicated by Arabic numerals in round brackets at the right-hand edge of the page, without a leader line from the formula to its number. If the number does not fit on the formula's line, it is placed on the next line below the formula. When a formula is carried over, the position of the number should be at the level of the last line. The position of the number of a formula in a box is outside the box at the right-hand edge, opposite the main line of the formula. The position of the number of a fraction formula is placed in the middle of the formula's main horizontal bar.

The numbering of a group of formulas placed on separate lines and united by a brace (parenthesis) is done on the right. The tip of the brace is located in the middle of the group of formulas by height and points towards the number, which is placed opposite the tip of the brace at the right-hand edge of the page.

Formula variants of a previously given basic formula may be numbered with an Arabic numeral and an upright lower-case letter of the Latin alphabet, written together with the number. For example: (14a), (14b).

Continuous (through) numbering of formulas is used in small works, where a limited number of the most important formulas are numbered. The same numbering can also be used in more voluminous works, if there are not too many numbered formulas and some chapters contain few references to formulas from other chapters.

When referring to a particular formula, its number is given in exactly the same graphic form as after the formula, i.e. Arabic numerals in round brackets. For example: in formula (3.7); from equation (5.1) it follows that...

If a reference to the number of a formula falls inside an expression enclosed in round brackets, it is recommended to replace them with square brackets. For example: Using the expression for the divergence [see formula (14.3)], we obtain...

At the end of formulas and in the text preceding them, punctuation marks are placed in accordance with the rules of punctuation.

A colon before a formula is placed only in those cases where it is required by the rules of punctuation:

a) the text before the formula contains a generalizing word;

b) this is required by the construction of the text preceding the formula.

Punctuation marks between formulas that follow one another and are not separated by text are separated by a comma or a semicolon. These punctuation marks are placed directly after the formulas, before their number.

Let us consider the general rules for the presentation and formatting of individual types of illustrative material.

A scholarly work must be illustrated on the basis of a definite general conception, according to a carefully thought-out thematic plan, which helps to avoid random illustrations linked to secondary details of the text and to prevent unjustified omissions of illustrations for the most important topics. Each illustration must correspond to the text, and the text to the illustration.

All illustrations in a scholarly work must be numbered. The numbering is usually continuous, i.e. running through the whole work. If there is only one illustration in the work, it is not numbered.

References are made in the text to illustrations, containing the serial numbers under which the illustrations are placed in the scholarly work.

References should not be formatted as independent phrases that merely repeat what is contained in the caption. At the point where the subject matter relates to the topic connected with the illustration, a reference is placed either in the form of an expression enclosed in round brackets "(Fig.3)", or in the form of a phrase such as: "...as can be seen in Fig.3" or "...as is evident from Fig.3".

Each illustration must be provided with a caption beneath it, which must correspond to the main text and to the illustration itself.

The caption under an illustration usually has four main elements:

- the name of the graphic subject, denoted by the abbreviated word "Fig. ";

- the serial number of the illustration, which is indicated without the number sign, in Arabic numerals;

- the thematic heading of the illustration, containing text characterizing what is depicted in the most concise form;

- the explication, which is constructed as follows: details of the subject are denoted by numbers, then these numbers are carried into the caption, accompanied by text. It should be noted that the explication does not replace the general name of the subject, but merely explains it.

The main types of illustrative material in scholarly works are: a drawing, a technical illustration, a schematic, a chart and a graph.

A drawing is used when it is necessary to depict the construction of a technical device, mechanism or their parts as accurately as possible. Any drawing must be made in exact accordance with the rules of drafting and the requirements of the relevant standards.

The names of assemblies and parts are usually not written, and if, according to the content of the text, it is necessary to indicate individual parts, they are numbered on the drawing with Arabic numerals. The decoding of these numbers (positions) is given either in the text in the course of the exposition, or in the caption beneath the drawing.

Technical illustrations are used in scholarly works when it is necessary to depict a phenomenon or object the way we perceive it visually, but only without excessive details and particulars. Such illustrations are usually executed in axonometric projection, which makes it possible to depict the object most simply and accessibly. Despite its simplicity, a technical illustration has broad cognitive potential.

With the help of a technical illustration, the shape, structure and arrangement of objects can be depicted with a greater degree of clarity. It helps to easily eliminate everything unnecessary that hinders understanding of the essence of the matter, and to highlight the main parts of what is depicted, showing a mechanism or its part in cross-section.

A schematic is an image that conveys, usually by means of conventional symbols and without observing scale, the basic idea of some device, object, structure or process, and shows the interrelation of their main elements.

In some scholarly works, the spatial schematics of various systems are depicted in the form of rectangles with simple connecting lines. Such schematics are usually called block diagrams. With this method of depicting schematics, there is no need to include in the manuscript separate illustrations depicting instruments and apparatus that are part of the schematic.

A chart - is one of the ways of graphically representing the relationship between quantities. Charts are compiled for the visual representation and analysis of mass data.

According to the form of construction, charts are distinguished as planar, linear and volumetric. In scholarly works, linear charts are the most widespread, and among planar ones - bar (band) charts and pie charts.

The results of processing numerical data can be presented in the form of graphs, that is, conventional representations of quantities and their relationships by means of geometric figures, points and lines. Graphs are used both for analysis and for enhancing the visual clarity of the material being illustrated.

In addition to the geometric image, a graph must contain a number of auxiliary elements:

- the general title of the graph;

- verbal explanations of the conventional symbols and the meaning of individual elements of the graphic image;

- the coordinate axes, the scale with its graduations and numerical grids;

- the numerical data, supplementing or clarifying the magnitude of the indicators plotted on the graph.

The axes of abscissas and ordinates of the graph are drawn as solid lines. No arrows are placed at the ends of the coordinate axes. In some cases, graphs are provided with a coordinate grid corresponding to the scale of the graduations along the abscissa and ordinate axes. The numerical values of the scale graduations of the coordinate axes are written outside the graph (to the left of the ordinate axis and below the abscissa axis). Fractional values of the scale divisions along the coordinate axes should be avoided.

On the coordinate axis, this factor should be indicated either alongside the letter designation of the quantity plotted along the axis, or introduced into the dimension of that quantity.

Along the coordinate axes, the conventional symbols and dimensions of the plotted quantities must be indicated in the accepted abbreviations. Labels relating to curves and points are left only in those cases where there are few of them and they are brief. Wordy labels are replaced by numbers, and the decoding is given in the caption beneath the figure. If labels cannot be replaced by symbols, they are written along the middle of the axis from bottom to top. The same is done with complex letter designations and dimensions that do not fit along the line of numerical values on the coordinate axes.

If the curve depicted on the graph occupies a small area, then to save space the numerical graduations on the coordinate axes can begin not from zero, but can be limited to those values within which the given functional dependence is being considered.

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Lectures and tutorial on "Fundamentals of Scientific Research and the organization of research activities"

Terms: Fundamentals of Scientific Research and the organization of research activities