This course aims to show how a living cell uses the principles of symmetry and conservation to carry out its functions. We will examine selected cellular structures and dynamical processes and construct computational models of them that are solved analytically, numerically or with computer simulations. The importance of dimensionality is illustrated by examining random walks in 1, 2 and 3 dimensions and two-dimensional fluid membranes that surround many cellular organelles and form the plasma membrane. The symmetry of a system usually changes when passing through a phase transition, and it is increasingly accepted that cells manipulate the phases of proteins in the cytosol to create membraneless organelles that are composed of intrinsically-disordered proteins (IDP). These organelles, which are also referred to as biomolecular condensates, carry out vital functions for the cell, but are implicated in neurodegenerative diseases such as Alzheimer's disease. They are three-dimensional, fluid networks formed by a process of liquid-liquid phase separation, and exhibit quite distinct structures and dynamics that are controlled by the thermodynamic properties of their constituent proteins within the crowded environment of the cytosol. We will construct models of IDPs and use simulations to quantitatively connect the structural properties of IDPs to the physical chemical properties of the condensates. Computer simulations are used to explore model systems in homework problems and a semester project. The primary goal of the course is to show students how nature uses symmetry and conservation to achieve specific cellular goals, and to understand how computer simulations can be used to study these processes.