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
The module "Experimental Physics" (AP80363) is taken by students in the department of Physics during the first semester of the second year. Having taken the modules of Classical Mechanics I and Electricity and Magnetism, these students have at this level enough background in Physics to do experiments, manipulate instruments and even design new experimental set up. At the end of the module, students should be able to
- Set up an experiment as per description in the laboratory protocol;
- Manipulate the instruments and record experimental data;
- Analyze experimental data and record correctly the outcome (with possible error);
- Write a report to communicate correctly the experimental results.
Note that one lab experiment can be run in one, two or more laboratory sessions depending on the legth of the maipulations or the level of difficulty.
Lecturer: Dr Mushinzimana Xavier
Office: 4R05
Emails: x.mushinzimana@ur.ac.rw
xaviermushi@gmail.com
Portable: +250 788837257
Introduction: thermodynamic and molecular-kinetic methods for studying thermal properties of matter; definitions and units of thermodynamics (substances, systems–fixed mass and fixed space, pressure, state of a system, process).
•Temperature: the zero law of thermodynamics; the constant-volume gas thermometer, the temperature scales, and thermometers.
•Thermal expansion of solids and liquids
•Heat: the mechanical equivalent of heat; specific heat; calorimetry; heat transfer modes.
•Macroscopic and microscopic descriptions of an ideal gas: mass and size of molecules; bases of molecular-kinetic theory; equation of state of an ideal gas; constant-volume, constant-temperature and constant-pressure processes, a molecular model for the pressure of an ideal gas; mean energy of molecules; the number of degrees of freedom; molecular interpretation of temperature; the mean velocity of the molecules; the root-mean-square (rms) speed; the most probable velocity; the Maxwell distribution.
This course provides a fundamental understanding of fluid mechanics. Starting from the definition of a fluid, theory will be build up in order to describe, characterize, analyze and understand the behavior of fluids (gases, liquids) in motion or static. Mechanics of fluids is a fundamental subject and one that finds many applications in meteorology and in aeronautics. In engineering several industrial and technological applications are found from ship design to pipe modeling.
The following topics will be covered:
Introduction: Basic concepts of fluid mechanics Fundamental term; Physical value; Fluids and their properties; Forces inside fluid.
Fluid Statistics: Pascal’s law; Euler’s equation of fluid statics; Measurement of pressure; Relative statics of fluid-constant acceleration, rotation; Forces of hydrostatic pressure; Buoyancy; Flotation; Stability. Surface tension' Capillary Action and Cavitation.
Fluid Kinematics: Euler and Lagrangian specification of fluid flow; Streamlines; Pathlines; Stream surface; Stream tube; Mass/volume flow; Control volume.
Fluid Dynamics: Hydrodynamic limit - deriving fluid equations; Mass, momentum and energy conservation; Navier-Stokes’s equations; Euler’s and Bernoulli’s equations for Ideal fluid flow and applications; Streamfunctions for incompressible flows and exact solutions; Potential flow, irrotational flow and velocity potential formulation; Vorticity dynamics; Real fluid flow: Viscosity. Determination of losses; Reynolds experiment; Laminar and turbulent flow; Boundary layer and viscosity; Velocity profile; Losses in pipes; Frictional losses; Moody’s diagram; Local losses; Coefficients of resistance; Introduction to multi-scale turbulence. Transport in turbulent flows.