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...determine the internal structure of Europa (Figure 2). Models have suggested that Europa has a metallic core surrounded by a rocky layer, like the Earth. This, plus an understanding of the moon’s physical properties, such as density and radius, have allowed scientists to constrain the depth of Europa’s ocean. Current estimates suggest the water-ice layer is ~100 km...

...determine whether a given set and binary operation form a group by checking group axioms describe the symmetries of some bounded three-dimensional figures...Introduction to group theory: Link to course PDF - Click here to access the course materials...Introduction to group theory: Conclusion - Following completion of this free OpenLearn course, Introduction to group...

...determine whether or not they are isomorphic express products of elements of a group defined by generators and relations in appropriate standard form recognise the dihedral and dicyclic groups when described using a standard form...Group theory: Link to course PDF - Click here to access course material...Group theory: Conclusion - Following completion of this free...

...determines stationary paths of a functional to deduce the differential equations for stationary paths in simple cases use the Euler-Lagrange equation or its first integral to find differential equations for stationary paths solve differential equations for stationary paths, subject to boundary conditions, in straightforward cases...Introduction to the calculus of...

...determine multiplicative inverses, modulo n and use to solve linear congruences...Introduction to number theory: Link to course PDF - Click here to access the course materials...Introduction to number theory: Conclusion - Following completion of this free OpenLearn course, Introduction to number theory, as well as becoming proficient at modular arithmetic, you should find...

...determine whether an inviscid flow is incompressible understand how Euler’s equation is derived, what it represents, and use it to find the pressure distribution from a velocity...Kinematics of fluids: Link to course PDF - Click here to access course material...Kinematics of fluids: Conclusion - Successful study of this free OpenLearn course, Kinematics of fluids,...