Maths is the last subject that I am studying as a part of following some ideas based on the 12 week year.
Maths is useful for studying Chemistry, which in turn is to support sustainable marketing projects.
Obviously maths has some applications in digital marketing as well.
Getting Started
Beginning with maths used the same method as with biology.
The categories within mathemetics that ChatGPT chose were algebra, trigonometry, calculus, statistics and applied maths.
The Questions
The answers below are those given by ChatGPT.
Algebra
What is the order of operations in algebra?
Parenthesis, Exponents, Multiplication and Division (from left to right), addition and subtraction (from left to right).
Solve the equation 2π₯ + 5 = 13
The solve the equation, first subtract the five from both sides 2π₯ + 5 – 5 = 13 – 5
2π₯ = 8
π₯ = 8 Γ· 2
π₯ = 4
What is a variable?
A variable is a symbol that represents an unknown number that could change.
Simplify the expression 3(a + 4) – 2a
First we have to distribute the 3:
3a + 12 – 2a
Next combine similar terms:
(3a-2a) + 12
Simplified as:
a + 12
Resolve the quadratic equation π₯2 – 4x + 4 = 0
(π₯β2) (π₯β2) = 0
Therefore: π₯ β 2 = 0 e π₯ = 2
Trigonometry
What is an angle in trigonometry?
An angle is the measure of rotation necessary to bring a ray from an initial position to a final position around a fixed point, known as a vertex
What is the formula to calculate the hypotenuse of a right angle triangle using the Pythagoras theorem?
The formula is π = βπ2 + π2 where π is the hypotenuse and π and π are the sides.
Define the sine, cosine and tangent
- The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse
- The cosine of an angle is the ratio of the length of the side adjacent to the length of the hypotenuse
- The tangent of an angle is the ratio of the length of the opposite side to the adjacent side
Calculate the sine of an angle of 30 degrees
The sine of 30 degrees is .5
What is a right triangle?
It is a triangle that has an angle of 90 degrees.
Calculus
What is a function?
A function is a relation between two sets that maps each element of one set to exactly one element of another set
What is a derivative?
It is the rate of change of a function with respect to a variable
What is the derivative of the function π(π₯)=π₯2?
The derivative of π(π₯)=π₯2 is πβ²(π₯) = 2π₯
What is the Leibniz notation for derivatives?
The Leibniz notation for derivatives uses the symbol π/ππ₯ to indicate a derivative with respect to the variable π₯. For example ππ¦/ππ₯ represents the derivative of π¦ with respect to π₯.
Try this three page document that is apprently the Leibniz Notation Simplified. Without prior knowledge it does not seem so simple.
What does the derivative of a function at a point mean?
The derivative of a function at a point represents the slope of the tangent line to the graph of the function at that point, or the instantaneous rate of change of the function at that point
Take a look at this explanation – it appears there is quite a lot of prior knowledge required for this also.
Statistics
What is arithmetic mean?
The arithmetic mean is the sum of the values of a data set divided by the quantity of values in the the data set.
How do you calculate the mean of a data set?
To calculate the mean, first order the data from smallest to largest. If the quantity of values in the data set is odd it is the middle value, if the quantity of values in the data set is even, the median is the arithmetic mean of the middle two values.
What is standard deviation?
The standard deviation is a measure of dispersion of values in a data set around its average. It indicates how far values typically deviate from the mean.
What is the mode of a data set?
The mode is the value that appears with the most frequency in a data set.
What is the difference between probability and statistics?
Probability studies the possibility that an event occurs in a theoretical context. Statistics on the other hand involves the collection, analysis and interpretation of real data.
Applied Mathematics
What is an array?
It is a rectangular arrangement of numbers, symbols or expressions arranged in rows and columns.
What is a system of linear equations?
A system of linear equations is a set of two or more linear equations that have the same variables that must be solved simultaneously.
What is a vector?
A vector is a mathematical object that has magnitude and direction. It can be represented in coordinates as a sequence of numbers.
How do you represent a multiplication of arrays?
A multiplication of arrays is represented by multiplying the rows of the first array by the columns of the second array and adding the corresponding products.
What is solving systems of equations using the inverse of a matrix?
Solving systems of equations using the inverse of a matrix involves finding the inverse of the matrix of the coefficients of the system and multiplying it by the vector of constant terms to obtain the solution of the system.
Conclusion
An overall score of 79% and the fact that finding information does not equate to understanding suggests ChatGPT’s idea of maths for beginners was somewhat questionable.
For most things it is easy to find an answer, but finding a clear explanation is a bit more difficult.
It’s likely that explanations for the various topics assume, and probably rightly so, the reader has prerequisite knowledge.
The goal for the following 11 weeks will be to refine the method and explore the prior knowledge.
No doubt it will barely come close for some topics, but let’s see what happens.