Perhaps the biggest barrier faced by the beginning student and their faculty mentors is not knowing where to begin. Accessible topics for new student researchers are often hard to find, even for experienced teachers, and finding unanswered questions that are well suited to student projects is time consuming. Accordingly, the maingoal of these two volumes is to expand research opportunities in mathematics for the beginning student by removing this significant hurdle. Specifically, we seek to provide community college students, early college students, and perhaps even advanced high school students everything they need to initiate research projectswith or without a faculty mentor, and to foster independence in research.Each chapter in these two volumes is a self-contained, accessible article that provides ample background material, recommendations for further reading, and perhaps most importantly, specific projects that can be pursued immediately upon reading the chapter.What makes these volumes different from other FURM volumesis that the chapters have been written for the beginning student by minimizing the number of prerequisites. Indeed, many of the chapters require no prerequisites other than a desire to pursue mathematics, and even the most ambitious chapters requireno more than linear algebra or introduction to proofs, both of which are typically sophomore-level classes.This volume is geared towards students with minimal experience beyond traditional high school mathematics. For the reader’s ease, we roughly order the chapters by prerequisite. The first four chapters require only high school algebra, the fifth chapter precalculus, the sixth a little probability and programming, the seventh andeighth some exposure to calculus, and the ninth a brief introduction to proof.