Charting Your Course: Mathematics vs. Statistics

Mathematics can be defined as a scientific study of quality, structure, spatial relationships, and integral and differential powers. All these subsets of mathematics form the four main branches of mathematics, number theory, algebra, geometry, and arithmetic math respectively. Mathematics can be further divided into pure mathematics and applied mathematics.

Statistics can be divided into inferential and descriptive statistics. Inferential statistics is the designated field that actively uses analytical tools and formulae to conclude a particular population through a specific sample size. Whereas, descriptive statistics are all about understanding the brief informational coefficients to effectively summarise and formulate the results through a given data set for the studied population.

B.Sc Mathematics vs. B.Sc Statistics: Course Duration and Eligibility

B.Sc Mathematics and B.Sc Statistics programmes have been designed 3-year extensive curriculum, that is 6 semesters to be precise. The course syllabus is vast and inclusive of theoretical and practical learning exposure for the students.

Eligibility criteria for B.Sc Mathematics: 12th Grade with Mathematics or equivalent studies completed with a percentage falling under the cut-offs as listed by the University.

Eligibility criteria for Statistics: 12th Grade with Mathematics or equivalent studies completed with a percentage falling under the cut-offs as listed by the University.

B.Sc Mathematics vs. B.Sc Statistics: Course Curriculum

The 3-year curriculum of both B.Sc Mathematics and B.Sc Statistics has been designed with much precision and care to cover all the major aspects of both subjects.

Mathematics Course Curriculum

Semester 1

1. Algebra
2. Differential Calculus & Vector Calculus
3. Vector Analysis & Geometry
4. Integral Calculus & Trigonometry

Semester 2

1. Advanced Calculus
2. Mathematical Methods
3. Differential Equations
4. Mechanics

Semester 3

1. Mechanics II
2. Differential Equations II
3. Analysis I

Semester 4

1. Vector Analysis
2. Differential Equations III
3. Analysis II

Semester 5

1. Numerical Methods
2. Numerical Methods Practical using C
3. Algebra III
4. Analysis III

Semester 6

1. Probability Theory
2. Linear Programming and Optimisation
3. Algebra IV
4. Analysis IV

Statistics Course Curriculum

Semester 1

1. Descriptive Statistics I
2. Calculus 
3. Inequalities  
4. Demoivre’s theorem
5. Probability and Probability Distributions I   
6. Linear Algebra and Population Statistics
7. Equations theories

Semester II

1. Descriptive Statistics II
2. Sampling Distributions and Statistical Infer
3. Differential Calculus
4. Review of Differential Equations
5. Probability and Probability Distributions II
6. Mathematical Analysis
7. Review of Integration and Definite Integrals

Semester III

1. Linear Algebra
2. Probability Theory   
3. Random Variables  
4. Expectation of Random Variable and its Properties 
5. Demography and Vital Statistics
6. Statistical Computing and Numerical Analysis Using C Programming
7. Design of Experiments and Sample Survey Methods
8. Measures of Location (or Central Tendency) and Dispersion
9. Multivariate Analysis and Large Sample
10. Official & Economic Statistics and Statistical Quality Control
11. Sampling Distributions
12. Mathematical Analysis 
13. Survey Sampling and Indian Official Statistics

Semester IV

1. Statistical Methods
2. Index Numbers
3. Mathematical Finance
4. Demand Analysis
5. Linear Models
6. Statistical Quality Control
7. Programming Language C
8. Utility and Production Functions
9. Time Series Analysis and Sample Survey Methods
10. Statistical Inference-I and Sampling Distributions
11. Index Numbers and Time Series Analysis
12. Time Series

Semester V

1. Statistical Inference-II
2. Sample Surveys
3. Basic Sampling Methods
4. Stratified Random Sampling 
5. Linear Models and Regression
6. Stochastic Processes and Queuing Theory
7. Statistical Computing Using C/C++ Programming
8. Sampling Theory, Time Series, Index Numbers, and Demand Analysis  
9. Statistical Quality Control and Reliability
10. Biostatistics - I 
11. Actuarial Statistics - I
12. Fundamental Theorem of Algebra and its Consequences 

Semester VI

1. Design of Experiments
2. Numerical Analysis
3. Inverse Interpolation
4. Numerical Integration
5. Multivariate Analysis and Nonparametric Methods
6. Data Interpretation
7. Mathematics
8. Design of Experiments, Vital Statistics, Official Statistics and Business Forecasting
9. Operations Research
10. Biostatistics - II
11. Actuarial Statistics - II
12. General Linear Models

B.Sc Mathematics vs. B.Sc Statistics: Career Opportunities

Mathematics and statistics are interrelated with distinct areas of study and different focal points of approach. After pursuing a bachelor's programme in the respective subjects, Mathematics and Statistics can be studied further by taking up the masters programming designed with a course curriculum for 2 years followed by research programmes if interested.
Below listed are the career prospects upon pursuing Mathematics and Statistics:

Mathematics

1. Academicians: They are involved in course curriculum building, researching, imparting knowledge to students, and being research guides
2. Data Science Associate: Deals with analysing large data and understanding the latest trends by using advanced computer and mathematical models
3. Statistician: A statistician analyses and compiles large statistical data to meaningful resources and conclusions
4. Mathematician: Make use of high-level mathematical principles and knowledge to solve real-world problems
5. Management Sector: Uses their mathematical knowledge to solve financial problems and calculative errors
6. Market Research Analyst: Helps in analysing the statistical data and predicts the market condition (rise and fall)

Statistics

1. Business Data Analyst: Helps in understanding and analysing the probable mistakes in the business structure and works on possibilities to maximise revenue
2. Manufacturing Industry: Helps with collecting customer feedback, understanding the complaints, and identifying the scope of improvements
3. Engineering Sector: Creates statistical surveys, experiments, and observational studies to collect data and formulate the results
4. Marketing Sector: Helps in identifying the market trends, analyses the condition, and predicts future market conditions
5. Health and Medicine: Analyses the risk factors with the change of health policies, and introduction of new medicines and assesses the quality and safety of the health care systems
6. Genetics Research Support: Helps to formulate the results and carry out various co-relation experiments
7. Academics: They are involved in course curriculum building, researching, imparting knowledge to students, and being research guides

In short

Mathematics and statistics tend to overlap in multiple areas but still are standalone subjects having an impactful say in every other field or domain. Having a great understanding and applying power in mathematics and statistics can provide extra room for the norm of improvisations. Statistics helps with analysing and predicting the probability of situations, whereas mathematical principles help in effectively finding the metrics to solve the consequences. Mathematics and statistics are important by themselves with several career options, thereby choosing either one of them as your major course can open a world of opportunities for you.