This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

Students are challenged to design, build and test small-scale launchers while they learn and follow the steps of the engineering design process. For the challenge, the "slingers" must be able to aim and launch Ping-Pong balls 20 feet into a goal using ordinary building materials such as tape, string, plastic spoons, film canisters, plastic cups, rubber bands and paper clips. Students first learn about defining the problem and why each step of the process is important. Teams develop solutions and determine which is the best based on design requirements. After making drawings, constructing and testing prototypes, they evaluate the results and make recommendations for potential second-generation prototypes.