1.3. Basic Mathematica rules

• Mathematica is constructed of two main modules: Front End (user interface) and Kernel (calculations core).
• Documents created with the system are called Notebooks and are files with an .nb extension, i.e.Primer.nb, 12my.nb etc. They are managed through the File menu.
• There is a possibility for simultaneous work with many documents by using the Window menu. The memory for the variables and their values is common.
• The text in the document can contain command lines, graphics, system results etc. and is organized in separate Cells. Every cell is processed as a whole. Different cells are designated in the right hand end of the work screen with a large closing square bracket ].
• Managing cells is done with the menu Cell. Cells can be formatted, grouped, ungrouped, merged, separated, closed, opened etc.  The selection of more cells is possible by pressing and holding down the CTRL key.
• Inputting formulas can be done in several ways. The most popular are: a) using palettes of mathematical symbols and built-in functions, found in the File/Palettes menu, as an example:    or b) typing in the corresponding text operator: Integrate[ f, { x, a, b} ] .
• Mathematica is an interpreter. The user sets command line grouped in a cell, where every operator is called Input, and the system carries out all separate lines, called Out with a number, i.e. Out[123]. Cycles are an exception.
• In the working session all inputs and outputs are saved by the system and can be used with their corresponding numbers in accordance to the order in which they are executed.  
• Executing the commands in the current cell is done by pressing the SHIFT and ENTER keys simultaneously.
• Calculations can be done with an arbitrary number of digits. To do this the command can be set as N[ command, number of digits]. The decimal digits are six by default.
• When there are long calculations the system displays it with a double bracket  ]] on the right hand side of the work field.
• Calculations are interrupted through the Action/Interrupt menu or by pressing Alt and ‘.’ simultaneously.
• A line, cell, group of cells or the whole notebook can be repeatedly executed simultaneously in any order.
• While typing bear in mind that the system is case sensitive: CoCa-CoLa is different from Coca-Cola.
• System functions must always start with a capital letter and their arguments must always be in square brackets, i.e. Plot[arguments,...].
• It is recommended that variable names, graphs and other user objects start with a non-capital letter. The name begins with a letter which is followed by an unlimited number of letters and/or numbers.
• The command line (operator) can contain  built-in functions, user functions, variables, constants etc. Variables and build-in functions do not need to be depicted beforehand by the user, since the system defines their type according to their initial assumptive meanings, i.e. whole number, complex number, symbol, list, graph, matrix etc.
• In order to master Mathematica faster and to the fullest it is recommended to use the extremely rich system Help and the full version of the built-in manual made by the creator of Mathematica - Steven Wolfram.