Among the topics covered in this introductory text are: asymptotic theories of definite integrals containing a parameter; ordinary differential equations; and sums and sequences. Special functions are introduced in chapter two and developed throughout the text.

This text introduces abstract algebra using familiar and concrete examples that illustrate each new concept as it is presented. It includes the coverage of such topics as the role of careful proof in algebra; linear algebra as grounded in geometry; groups as expressions of symmetry; subgroups and subsystems leading to lattice theory; and more.