The purpose of this text is to properly prepare students in the logical thinking abilities required to comprehend and explain basic mathematical ideas and proofs—acquired abilities that are essential for success in the upper-class mathematics curriculum. The work covers discrete and continuous mathematics, allowing teachers to highlight one or cover the basics of both. It begins with a discussion of mathematical terminology and proof strategies (including induction), applies them to simple problems in elementary number theory and counting, and then develops further proof strategies through significant discrete and continuous mathematics topics. The energizing exercises are praised for their superior caliber.