Enrolment options
This module equips students with the statistical and probabilistic reasoning skills essential to experimental and theoretical physics. It covers descriptive statistics (measures of central tendency and dispersion) and inferential statistics (confidence intervals and hypothesis testing), alongside the probability distributions most frequently encountered in physical measurement—binomial, Poisson, Gaussian (normal), and chi-square. Throughout, methods are grounded in physics contexts such as detector counting statistics, measurement uncertainty, and signal detection, so that students learn not just the mathematics but also how to apply it to real experimental data.
What You Will Learn
The course is organized into eleven units progressing from foundational to applied topics:
- Descriptive Statistics and Data Visualization—central tendency, dispersion, histograms, and error bars on experimental data
- Introduction to Probability Theory—sample spaces, conditional probability, and Bayes' theorem for updating results with new evidence
- Discrete Probability Distributions—Binomial, Poisson, and Chi-square, applied to detector efficiency and radioactive decay counts
- Continuous Probability Distributions—the Gaussian distribution, the Central Limit Theorem, and Z-scores
- Sampling Theory and Experimental Design—sample size determination and degrees of freedom
- Confidence Intervals—reporting measured physical constants with rigorous uncertainty
- Hypothesis Testing—Z-, t-, and chi-square tests, p-values, and the statistical threshold for discovery
- Tests of Significance and Goodness-of-Fit—comparing observed data to theoretical models
- Correlation and Regression Analysis—calibration curves and least-squares fitting
- Statistical Process Control—monitoring stability in instrumentation and an introduction to Monte Carlo methods
- Error Propagation and Uncertainty Analysis—combining and propagating measurement uncertainties, including weighted averages
Learning Outcomes
By the end of this module, students will be able to:
- Apply appropriate statistical methods according to data type and select suitable probability distributions for physical phenomena
- Perform descriptive and inferential statistical analyses, including confidence interval construction and hypothesis testing
- Fit models to experimental data, evaluate goodness-of-fit, and propagate measurement uncertainty
- Communicate statistical results clearly to specialist and non-specialist audiences, using appropriate software tools
Teaching and Assessment
Delivery is face-to-face lectures, computer practicals, and small-group problem-solving sessions (groups of 5), supported by problem sheets and worked examples.
Continuous assessment (assignments, quizzes, and mini-projects) and a final written examination each contribute 50% of the final grade, ensuring students demonstrate both conceptual understanding and applied problem-solving ability.
Facilitator: Dr. Rongin Uwitije
Department of Mathematics
Email: r.uwutije@ur.ac.rw or ruwitije@gmail.com