The primary objective of this course is to provide students with a comprehensive understanding of the research process. This will be achieved through a structured approach encompassing the following key elements: Acquiring Background Knowledge: Students will be introduced to the fundamental concepts, theories, and methodologies that form the foundation of the subject matter. Hypothesis Formulation: Under the guidance of the instructor, students will learn to formulate research hypotheses and conjectures related to specific problems within the field. Literature Review: Through rigorous exploration, students will examine existing literature and research pertaining to their selected problems to gain a comprehensive understanding of the current state of knowledge. Proof and Validation: Students will engage in the process of rigorously proving their conjectures, employing mathematical and analytical techniques. Scientific Writing: A critical component of this course, students will be required to draft research papers following the conventions of journal-style writing. This exercise aims to enhance their academic communication and writing skills. Oral Presentation: Students will hone their presentation skills by delivering an organized and well-structured presentation of their research findings, fostering the ability to communicate complex ideas effectively. To facilitate this learning journey, students will be provided with carefully crafted prompts to initiate their research projects. Additionally, groups will have the autonomy to select their research topics from a predetermined list of problems. This course aims to nurture students' research capabilities and equip them with the skills necessary to contribute to the field of study.