

Overview
This course is designed to provide a handson experience to the student for gaining insight into the world of data for building models; and for providing a glimpse into the practical power of the world of numbers. These models are relevant for some of the needs and challenges of India. A significant portion of the learning process is based on open ebooks that are highly interactive and that transfer knowledge into practice. This course aims to seamlessly blend theory and practice where often practical knowledge precedes theoretical insights. Additionally, the project and application oriented hands on learning process would introduce the joys and advantages of working cohesively and productively in groups to relate mathematics to real world problems. 

Objective & Expected Outcomes
Learning mathematics by connecting it to real life problems linked to society.
Extending blackboard teaching to solve practical problems using mathematics.
Triggering analytical thinking.
Encourage experimentation and handson projects mode of learning.
Appreciation of role of data, learn how to collect data and analyze it.
Correlate real world observations with the theoretical knowledge.
Mathematical analysis of data for simple quantitative inference.
The allocation of lectures is approximate and will have review sessions to make 14+2 weeks.

Themes & Subthemes
I. Numbers (6 lectures)
 Prime numbers
 Interesting properties of prime numbers without proofs
 Ramanujan's work on the Prime Number Theorem
 Euclid's division algorithm
 Mathematical illustration through intuitive examples
 Visualisation through tiling analogy
 Encryption and Prime numbers
 Gentle introduction of 2 x 2 matrices
Constructing the RSA Algorithm
Project Themes
 Ramanujan's work
 Implementations of RSA algorithms
 Other methods of encryption
II. Data and patterns (6 lectures)
 Historical perspective and importance of data
 Kepler's law for planetary orbits from Tycho Brahe's astronomical observation
 Ramanujan's work on Prime numbers through data
 Data collection techniques
 Formulation of problem – goals, targets
 Methods to collect data – questionnaire, observations, recording, etc.
 How much of data is enough for the given problem
 Population and sample
Project Themes
 Collecting and organising data in various situations through practical methods, from the
internet and from other sources.
 Use of spreadsheets for practical work related to the above concepts.
III. Statistics (8 lectures)
 Organisation of data
 Frequency table
 Grouping
 Visualisation of data
 Pictorially displaying data: dot plots, bar graphs, line graphs, pie charts
 Misinterpretation of data by distorting the figures: Scaling and axis manipulation,
Line graphs and cropping
 Analysis of data
 Mean, median, mode, variance, standard deviation.
 Histogram, skewed distribution
 Comparing two distributions
Project Themes
 Statistical analysis of daily life data
 Statistical analysis of stock market data
 Statistical analysis of weather data
 Statistical analysis of data for better governance
IV. Probability (4 lectures)
 Interpreting probability, Sample Space, Events
 Understanding the tossing of a coin and throwing of dice for large number of trials Probability in a situation where there are equallylikely outcomes
 Probability of two independent events
V. Project Themes
 Compute probabilities from insufficient information
 Validity of computed probability

Suggestive Project Projects

Reading List
Printed Material
 Berlinghoff, W. P., Grant, K. E., & Skrien, D. (2001). A Mathematics Sampler:
Topics for the Liberal Arts (4 ed.). Ardsley House.
 Maki, D. P. (2006). Mathematical Modeling and Computer Simulation (1 ed.). Thomsons Brooke Cole.
 Parks, H. M. (2007). A Mathematical View of Our World (1 ed.). Thomsons Brooks Cole.
 Staszkow, R., & Bradshaw, R. (2004). The Mathematical Palette (3 ed.). Thomsons Brooks Cole.
 Tannenbaum, P. (2010). Excursions in Modern Mathematics. Pearson.

Eresources:

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