This course is designed to provide a hands-on 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 e-books 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 hands-on 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 & Sub-themes
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
- 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
- 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
- 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
- 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 equally-likely outcomes
- Probability of two independent events
V. Project Themes
- Compute probabilities from insufficient information
- Validity of computed probability
Suggestive Project Projects
- 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.
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