MyPyFriend - Math and Python

Math in Section 1: Variables

In math, we have the concept of variables, which are used to express unknown values while solving problems. In math, we consistently see variables represented with the letter "x", or other letters, such as "y" or "a". We can also see variables represented with symbols, such as alpha or beta. In Python, the logic is practically same. We have variables, just like in math, that are represented by a letter or text (such as "x") and have values set using an equals to sign.

x = 360

text = "hello!"

The difference between Python variables and mathematical variables largely stems from the fact that in math, using variables to represent text values is far more unlikely then it is in Python, where all data types (strings, integers, booleans, etc.) are represented using variables. Additionally, just like how the letters e and i have special values in algebra and are usually not used as variables, π and e are also used in special instances with the Python math module and represent specific values.

Variables also allow for one thing in math that is also seen in Python: variables change verbal expressions into algebraic expressions, that is, expressions that are composed of letters that stand for numbers. For example, in both Python and mathematics variables can express the verbal expression the sum of a number and 5 as:

x + 5 or 5 + x

The value of six times a number can be expressed as an algebraic expression as:

In both mathematics and Python.

Math in Section 2: Math and Numbers

The section in the course most related to mathematics, numbers and mathematical operations share various similarities with each other. First of all, both Python and math share the same number set which is the integer number set. However, Python does not divide the integer number set any further, unlike in math where there also exists whole and natural numbers. Additionally, in mathematics, several number sets such as natural numbers, integers, rational numbers, irrational numbers exist. In Python, there are only two number sets: integers and floating point numbers. Floating point numbers cover rational numbers, however, in Python π and e are both rounded so they can be considered floating point numbers. Therefore, it can be argued that floating point numbers also cover irrational numbers.

Additionally, both math and Python are similar with the operators they use and the operation order. In math, the operators used for addition (+), subtraction (-) and division (/) are all the same in Python. Although internationally some countries use different methods to show multiplication, it can also be argued that the multiplication sign used in Python (*) shows similarities to many countries. For example, in Turkey, using a point is the preferred way of showing multiplication, which the asterisk may represent. The operation symbol which shows the most difference is the exponentiation symbol, using two asterisks (**). The order of operations in Python is the exact same as the one in normal mathematics and is the PEMDAS order of operations. For example the following operation of:

27 / (8 - 5) * 2

will result in the result in Python and math which will be 18.

Python's randomization and modulo methods are entirely dependent on math, as well. The modulo method is entirly reliant on the mathematical concept of divisibility. To better estimate the result of a modulo method, one must know the rules of divisibility for then numbers they are testing. For example, an even number modulo 2 will always give back a result of 0, as an even number is divisible by 2. The operation of 546 modulo both 3 and 6 will also give a value of 0 and any user familiar with divisibility in mathematics can easily work this out. Additionally, Python's randomization feature and module allows for the inclusion of the mathematical concept of probability into our code. By being able to generate random numbers, we are given the ability to add randomness into our code not only in terms of integers and floating point numbers but we can also select random elements of a list by generating random numbers.

Math in Section 4: Python Conditional Flow

Within this section, the incorporation of comparison and particularly logical operators are where math shine. Comparison operators within Python are very similar to those in mathematics and are in many cases the exact same as in mathematics. The greater than (>) and the less than (<) signs are the same in both Python and math, also representing the same thing. The only comparison operator showing a difference from those in mathematics is the not equal to sign, represented as !=, rather than as ≠. Additionally, the method of checking equality in Python is done using to equals to signs (==), which shows a difference from mathematics.

The usage of logical operators in Python incorporates an important mathematical concept: logic. Math has several propositions under the concept of logic. For example, "1 + 2 = 3" and "4 is even" are two mathematical propositions which are true, while all prime numbers are even is false. In logic we are often not interested in these statements themself, but how true and false statements are related to each other. This is how we also obtain booleans in Python. So the values of mathematical propositions (True and False) are booleans in Python. These mathematical propositions can be linked together through different operators. We have the "or" operator, represented by ∨, the "and" operator, represented by ∧ and several others in mathematical logic. All of these translate into the logical operators within Python exactly. The concept of De Morgan's laws is mathematics also translates into Python as the not operator.

Math in Section 5: Lists and Tuples

Lists within Python show pratically the same characteristics of sets in mathematics. In mathematics, sets are represented as a collection of well-defined objects or elements which does not change from person to person. These could include the capital cities of Europe, natural numbers, letters of the alphabet and anything else which is well-defined and isn't variable. In Python, lists also represent the same thing and the notation of lists is even the same as the notation of sets, represented by curly brackets ({}). Therefore, Python uses the mathematical concept of sets as one of its most fundamental data types.

For example, below is the notation of a list in Python:

countries = {"France", "Germany", "Italy", "Spain", "UK", "Turkey"}

If we were to notate that list as a set in mathematics, we would receive the exact same result.

Math in Section 8: Functions

The logic behind mathematical functions and Python functions are nearly identical. In mathematics, functions relate an input to an output and they are honestly like machines which take an input and result an output based on a certain condition. For example, if we have a function that will multiply the input by two, all of the outputs are going to be the inputs multiplied by two and will generate an even number. Though functions can receive any name (f and g are the most common ones), they have place holder for the inputs in the form of x and are defined as below:

f(x) = 2x

Just in terms of these qualities alone, mathematical functions show a lot of similarities with Python functions. First of all, Python functions also take in inputs and have the purpose of creating an output based of those inputs. Additionally just like how in mathematical functions the X is a place holder for the actual data, in Python functions parameters are place holders for the inputs, which are the arguments. For example:

def multiply(x):

return x * 2

multiply(4)

Here, the x in the expression def multiply(x) is a place holder, so a parameter, for the actual data which is 4. The output of this will be 8, as all of the outputs are the inputs multiplied by two as if we just wrote f(x) = 2x.

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