**Added new assignments for +1, +2 and Graduate classes.**

## Ashwani Goyal

Department of Mathematics

S U S College,

Sunam—148028 Punjab

### Contact Information

Mobile: + 91 9872876027

Land Line: 01676228027

Email ID:goyal.sunam@gmail.com

**New batches will start soon.**

Mathematics is the science of numbers and there are several different branches
of mathematical science including algebra, geometry, and calculus. The Merriam-Webster
dictionary defines mathematics as the science of numbers and their operations, interrelations,
combinations, generalizations, and abstractions and of space configurations and
their structure, measurement, transformations, and generalizations.

Mathematics is not an
invention. Discoveries and laws of science are not considered
inventions. Inventions are material things and processes. However, there is a history
of mathematics, a relationship between mathematics and inventions, and mathematical
instruments are considered inventions.

**Mathematics**– study of quantity, structure, space, and change. Mathematicians seek out patterns,and formulate new conjectures.

- Arithmetic – oldest and most elementary
branch of mathematics, involving the study of quantity, especially as the result
of combining numbers. The simplest arithmetical operations include addition, subtraction,
multiplication and division.
- Algebra – branch of mathematics concerning
the study of the rules of operations and relations, and the constructions and concepts
arising from them, including terms, polynomials, equations and algebraic structures.
- Calculus – branch of mathematics focused on
limits, functions, derivatives, integrals, and infinite series. Calculus is the
study of change,
^{[3]}in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. - Category theory –
- Discrete mathematics – study of
mathematical structures that are fundamentally discrete rather than continuous.
In contrast to
real numbers that have the property of varying "smoothly", the
objects studied in discrete mathematics – such as integers, graphs, and statements
in logic do not vary smoothly in this way, but have distinct, separated values.
- Combinatorics – branch of mathematics
concerning the study of finite or countable discrete structures.
- Geometry – one of the oldest branches of mathematics,
it is concerned with questions of shape, size, relative position of figures, and
the properties of space.
- Trigonometry – branch of mathematics that
studies triangles and the relationships between their sides and the angles between
these sides. Trigonometry defines the trigonometric functions, which describe those
relationships and have applicability to cyclical phenomena, such as waves.

**Other mathematical sciences**– academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper.- Statistics – study of the collection, organization,
and interpretation of data.It
deals with all aspects of this, including the planning of data collection in terms
of the design of
surveys and
experiments.
- Regression analysis – techniques
for modeling and analyzing several variables, when the focus is on the relationship
between a dependent variable and one or more independent variables. More specifically,
regression analysis helps one understand how the typical value of the dependent
variable changes when any one of the independent variables is varied, while the
other independent variables are held fixed.
- Probability – way of expressing knowledge
or belief that an event will occur or has occurred. The concept has an exact mathematical
meaning in probability theory, which is used extensively in such areas of study
as mathematics, statistics, finance, gambling, science, artificial intelligence/machine
learning and philosophy to draw conclusions about the likelihood of potential events
and the underlying mechanics of complex systems.

- Statistics – study of the collection, organization,
and interpretation of data.It
deals with all aspects of this, including the planning of data collection in terms
of the design of
surveys and
experiments.