Maths For Ds

Chapter 1.1 : Foundations – Mathematics and Statistics: (Basic Mathematics, Algebra and Calculus, Statistics, Probability, and Hypothesis testing)

Vidya RajasekaranLast Seen: Mar 11, 2024 @ 1:05am 1MarUTC
Vidya Rajasekaran

22nd December 2023 | 6 Views

Info: This Creation is monetized via ads and affiliate links. We may earn from promoting certain products in our Creations, or when you engage with various Ad Units.

How was this Creation created: We are a completely AI-free platform, all Creations are checked to make sure content is original, human-written, and plagiarism free.


1. Algebra:

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. Here are some fundamental algebraic concepts:

Variables and Expressions: Variables represent unknown or changing quantities. Expressions are combinations of variables, numbers, and operations (addition, subtraction, multiplication, division).

a + b (addition of two numbers)
a − b (subtraction of two numbers)
a × b or a * b (multiplication of two numbers)
a / b   (division of two numbers)

Example : 

Equations and Inequalities: Equations express the equality of two expressions. Inequalities express relationships where one side is greater than or less than the other.

(linear equation)

  (quadratic equation)


Example : 

Functions:  Functions describe relationships between variables. They have inputs (independent variable) and outputs (dependent variable).

(linear function)

(quadratic function)

Example : 

2. Calculus:

Calculus involves the study of rates of change and the accumulation of quantities. Key concepts include:

Limits and Continuity: Limits describe the behavior of a function as the input approaches a certain value. Continuity ensures that there are no abrupt jumps or holes in the graph of a function.

(limit of a function)

is continuous at

Derivatives: Derivatives measure the rate at which a function changes. They represent slopes of tangent lines to curves.

or (derivative of )

(power rule)

Example : 

Integrals: Integrals compute the accumulation of quantities and the area under curves. They are the reverse process of derivatives.

(indefinite integral)

Example : 

3. Statistics:

Statistics involves the collection, analysis, interpretation, presentation, and organization of data. Key concepts include:

Descriptive Statistics: Measures of central tendency (mean, median, mode). Measures of dispersion (range, variance, standard deviation).

Example : 

Inferential Statistics: Uses sample data to make inferences about a population. Includes hypothesis testing and confidence intervals.

Example : 

4. Probability:

Probability deals with the likelihood of events occurring. Key concepts include:

Probability Basics: Probability is a number between 0 and 1, representing the likelihood of an event. The sum of all probabilities in a sample space is 1.

Example : 

Random Variables and Probability Distributions: Random variables represent outcomes of a random process. Probability distributions describe the likelihood of different outcomes.

Example : 

Hypothesis Testing:

Hypothesis testing is a statistical method to make inferences about a population based on a sample of data. Key steps include:

Formulating Hypotheses: Null hypothesis (H0) and alternative hypothesis (H1).

Example : 

Choosing a Significance Level: Common levels include 0.05 or 0.01.

Example : 

Collecting Data and Calculating Test Statistic: Use statistical tests (t-tests, chi-square tests) to analyze data.

Example : 

Making a Decision: Compare the p-value to the significance level and make a decision about the null hypothesis.

Compare the p-value to the significance level (α)

Example : 

Compare the p-value to ( to accept or reject the null hypothesis.

Vidya RajasekaranLast Seen: Mar 11, 2024 @ 1:05am 1MarUTC

Vidya Rajasekaran



You may also like

Leave a Reply