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"description": "<h1>Program Prerequisites</h1><p style=\"font-weight: 400;\">Bachelor's degree in mathematics or closely related field.</p> <p style=\"font-weight: 400;\"> </p> <p style=\"font-weight: 400;\">Students admitted to the graduate program with regular status are expected to possess a solid foundation in undergraduate mathematics, including the calculus sequence, differential equations, and linear algebra. Additionally, they should demonstrate proficiency in constructing and understanding mathematical proofs, exhibiting a level of mathematical maturity comparable to that attained in an Advanced Calculus course, such as UCF’s <a href=\"https://sciences.ucf.edu/math/course/maa-4226-advanced-calculus-i/\">MAA 4226</a>.</p> <p style=\"font-weight: 400;\"> </p> <p style=\"font-weight: 400;\">For students needing additional preparation or further development of mathematical skills, the program offers remedial courses in the first semester, structured as split-level classes.</p><h1>Degree Requirements</h1><div><section><header data-test=\"grouping-0-header\"><div><h2 data-testid=\"grouping-label\"><span>Required Courses</span></h2></div><div><span>27</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\">Complete at least <span>9</span> of the following: <div><ul style=\"margin-top:5px;margin-bottom:5px\"><li><span><a href=\"#/courses/view/60ca7fb7e6bc7968ca73e8a4\" target=\"_blank\">MAA5237</a> <!-- -->-<!-- --> <!-- -->Mathematical Analysis<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/67531c9c3972fae43e6a7841\" target=\"_blank\">MAA6405</a> <!-- -->-<!-- --> <!-- -->Complex Analysis I<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fcaa38edf41a23ec7b6\" target=\"_blank\">MAS5311</a> <!-- -->-<!-- --> <!-- -->Algebra I<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fb960402b61fcae769e\" target=\"_blank\">MAD5205</a> <!-- -->-<!-- --> <!-- -->Graph Theory I<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fb8e6bc79ec1473e8a6\" target=\"_blank\">MAA6416</a> <!-- -->-<!-- --> <!-- -->Topology<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fe55ada37e038ec9f79\" target=\"_blank\">MTG5256</a> <!-- -->-<!-- --> <!-- -->Differential Geometry<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fc95ada374d7aec9f3b\" target=\"_blank\">MAS5145</a> <!-- -->-<!-- --> <!-- -->Advanced Linear Algebra and Matrix Theory<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fcd5ada37c20eec9f41\" target=\"_blank\">MAT5712</a> <!-- -->-<!-- --> <!-- -->Scientific Computing<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fc2a38edf2ea93ec7aa\" target=\"_blank\">MAP5336</a> <!-- -->-<!-- --> <!-- -->Ordinary Differential Equations and Applications<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fc360402b48e5ae76b4\" target=\"_blank\">MAP6356</a> <!-- -->-<!-- --> <!-- -->Partial Differential Equations<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/675312043bcc24b93e319d22\" target=\"_blank\">MAA5238</a> <!-- -->-<!-- --> <!-- -->Measure and Probability I<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li><li><span><a href=\"#/courses/view/60ca7fc35a158306459e706c\" target=\"_blank\">MAP6111</a> <!-- -->-<!-- --> <!-- -->Mathematical Statistics<!-- --> <span style=\"margin-left:5px\">(3)</span></span></li></ul></div></div></li></ul></div></div></section><section><header data-test=\"grouping-1-header\"><div><h2 data-testid=\"grouping-label\"><span>Electives</span></h2></div><div><span>30</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\">Earn at least <span>30</span> credits from the following types of courses: <div>advanced mathematical courses at the 6000 or 7000 level. This may include up to 9 credit hours from Independent Study (XXX 6908), Directed Research (XXX 6918), or Special Topics/Seminars (XXX 6939). Of the total required credits, at least 24 credit hours must be earned from courses offered by the Department of Mathematics. Any coursework taken outside the department requires prior approval from the graduate program director. \n6000-level core courses that were not used to meet the core course requirement may count toward the 30-credit-hour minimum of Electives.\n\nStudents' coursework must be planned in coordination with their Ph.D. advisor or the graduate program director.\n\nThe following is a list of regularly offered Elective courses:\n\nMAA6245 - Measure and Probability II (3)\nMAA6306 - Real Analysis (3)\nMAA6408 - Complex Analysis II (3)\nMAA6506 - Functional Analysis (3)\nMAA7239 - Asymptotic Methods in Mathematical Statistics (3)\nMAD6309 - Graph Theory II (3)\nMAP 7386 - Numerical Solutions of PDE (3)\nMAP6118 - Introduction to Nonlinear Dynamics (3)\nMAP6195 - Mathematical Foundations for Massive Data Modeling and Analysis (3)\nMAP6197 - Mathematical Introduction to Deep Learning (3)\nMAP6207 - Optimization Theory (3)\nMAP6218 - Stochastic Calculus (3)\nMAP6385 - Applied Numerical Mathematics (3)\nMAP6387 - Numerical Linear Algebra (3)\nMAP6416 - Applied and Computational Harmonic Analysis (3)\nMAP6445 - Approximation Techniques (3)\nMAP6469 - Bayesian Analysis and Approximation Theory (3)\nMAP7359 - Advanced Topics in Partial Differential Equations (3)\nMAS6312 - Algebra II (3)\nMTG6345 - Algebraic Topology (3)\n</div></div></li></ul></div></div></section><section><header data-test=\"grouping-2-header\"><div><h2 data-testid=\"grouping-label\"><span>Dissertation</span></h2></div><div><span>15</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\">Earn at least <span>15</span> credits from the following types of courses: <div>XXXX 7980 Dissertation Research 15 Credit Hours (minimum)\n</div></div></li></ul></div></div></section><section><header data-test=\"grouping-3-header\"><div><h2 data-testid=\"grouping-label\"><span>Examinations</span></h2></div><div><span>0</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div>No Rules</div><div><section><div><header><div><h2>Qualifying Examination</h2></div><div><span>0</span><span>Total Credits</span></div><div><button aria-label=\"Collapse\"><i></i></button></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\"><div>To complete the first training phase and advance in the Ph.D. program, students are required to pass two written Qualifying Examinations, administered by the Graduate Program Committee with support from Mathematics Graduate Faculty. These examinations are intended to assess the student’s mathematical rigor and analytical maturity by testing foundational concepts in Analysis and Linear Algebra, corresponding to contents covered in MAA 5237 – Mathematical Analysis and MAS 5145 – Advanced Linear Algebra and Matrix Theory.\nThe Qualifying Examinations are held twice yearly: just before the start of the Fall semester and at the beginning of the Spring semester. Eligibility to sit for the examination requires that students maintain a minimum program GPA of 3.0 on a 4.0 scale and submit a formal written request to take the examination at least thirty (30) days prior to the scheduled date.\nStudents are expected to pass both qualifying examinations by the end of their first year. Passing both exams is required to continue in the program beyond the second year. Although there is no limit on the number of attempts allowed for students into take each exam, students who do not pass both exams by the end of their second year will be dismissed from the program but may be eligible for an MS degree en route.</div></div></li></ul></div></div></div></section><section><div><header><div><h2>Candidacy Examination</h2></div><div><span>0</span><span>Total Credits</span></div><div><button aria-label=\"Collapse\"><i></i></button></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\"><div>The Candidacy Examination is a pivotal step taken prior to a student’s formal admission to Ph.D. Candidacy. Unlike exams based purely on textbook material, this examination focuses on advanced topics closely aligned with the student’s prospective dissertation project, often encompassing recent developments and ongoing research in the field. Its purpose is to ensure the student is well-prepared to undertake independent research and contribute meaningfully to the discipline.\nThis exam is administered by the Candidacy Examination Committee, composed of the student’s Ph.D. advisor and two other members of the Graduate Faculty. It comprises of two parts, a written report and an oral examination. \nThe written component of the exam must be submitted as a research report to the Candidacy Examination Committee, which will evaluate its breadth, depth, and relevance. If the report receives approval, the oral examination will be scheduled.\nThe oral examination is conducted privately and is not open to the public. The Candidacy Examination Committee determines the structure and duration of the exam. During this examination, students are expected to demonstrate mastery of the topics presented in their research report by responding to questions related to the subject matter. \nStudents must complete the Candidacy Examination before the end of their fourth year. Students are granted a maximum of two attempts to successfully pass the examination. Students who do not pass the Candidacy Examination within two attempts and before the end of the fourth year will be dismissed from the program but may be eligible for an MS degree en route.</div></div></li></ul></div></div></div></section></div></div></section><section><header data-test=\"grouping-4-header\"><div><h2 data-testid=\"grouping-label\"><span>Seminar Participation</span></h2></div><div><span>0</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\"><div>Ph.D. students in regular status are required to attend a significant portion of the seminars and colloquia hosted by the Mathematics Department. Students in their third year and beyond are also expected to present their research or independent study annually.</div></div></li></ul></div></div></section><section><header data-test=\"grouping-5-header\"><div><h2 data-testid=\"grouping-label\"><span>Admission to Candidacy</span></h2></div><div><span>0</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\"><div>Admission to Candidacy marks a significant milestone in a Ph.D. student’s academic journey, signifying the successful completion of required coursework and examinations needed for independent research. This status represents a transition from coursework to original research, granting students greater independence and responsibility in their academic pursuits. It reflects faculty confidence in the student's readiness to contribute meaningfully to their field, paving the way for intensive research opportunities, leading to the successful completion of their dissertation, the pinnacle of their academic achievement.\nRequirements for Admission to Candidacy\n1.\tCompletion of Coursework: Students must complete all required coursework, maintaining a minimum program GPA of 3.0 on a 4.0 scale. This includes both foundational and advanced classes, totaling a minimum of 57 credit hours. Of these, at least 21 credit hours must be earned from courses at the 6000 and 7000 levels.\n2.\tCandidacy Examination: Students must pass the Candidacy Examination, which, as described above, includes a written research report and an oral component. \n3.\tAdvisory Commitment: The dissertation advisory committee must be submitted and approved by the graduate program director. It consists of the PhD advisor, assisted by at least three other graduate faculties or scholars, with at least one of them external to the Department of Mathematics. \n4.\tProgram of Study: An approved program of study must be submitted. \nOnce admitted to candidacy, students are expected to focus on their dissertation research. </div></div></li></ul></div></div></section><section><header data-test=\"grouping-6-header\"><div><h2 data-testid=\"grouping-label\"><span>Dissertation </span></h2></div><div><span>0</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div>No Rules</div><div><section><div><header><div><h2>Dissertation Proposal Examination</h2></div><div><span>0</span><span>Total Credits</span></div><div><button aria-label=\"Collapse\"><i></i></button></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\"><div>After successfully passing the Candidacy Examination, the student is required to prepare a Dissertation Proposal and present it orally to the Dissertation Advisory Committee for approval. The proposal should comprehensively outline the research conducted to date, as well as provide a detailed agenda for the research intended to be completed for the dissertation.\nIn addition to demonstrating a high level of mastery in the relevant area of study, the proposal must adhere to rigorous academic standards regarding correctness and the suitability of the proposed dissertation topic. The presentation must also meet the current standards for professional presentations within the discipline of mathematics.\nTo successfully complete the Dissertation Proposal Examination, the presentation must be evaluated and approved by a majority of the Dissertation Committee as meeting the examination requirements. This examination must be completed within 12 months of passing the Candidacy Examination and no later than the end of the fifth year of graduate study. Candidates are allowed a maximum of two attempts to pass this examination. Students who do not pass the Dissertation Proposal Examination within two attempts and before the end of the fifth year will be dismissed from the program but may be eligible for an MS degree en route.</div></div></li></ul></div></div></div></section><section><div><header><div><h2>Dissertation Defense</h2></div><div><span>0</span><span>Total Credits</span></div><div><button aria-label=\"Collapse\"><i></i></button></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\"><div>Upon completion of the student's research, the Dissertation Advisory Committee will schedule an oral defense of the dissertation. This defense serves as a formal presentation in which the student articulates their research findings, methodology, and contributions to the field.\n\nThe successful completion of the dissertation defense marks the culmination of the student's academic journey, demonstrating their preparedness to contribute original research to the academic community and/or to take on leadership roles in industry, government, or other sectors where advanced mathematical thinking is essential.</div></div></li></ul></div></div></div></section></div></div></section><section><header data-test=\"grouping-7-header\"><div><h2 data-testid=\"grouping-label\"><span>Independent Learning</span></h2></div><div><span>0</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\"><div>The required 15 credit hours of dissertation will provide ample opportunities for students to gain the independent learning experience through studying published research papers and deriving, on their own, new and meaningful research results. </div></div></li></ul></div></div></section><section><header data-test=\"grouping-8-header\"><div><h2 data-testid=\"grouping-label\"><span>Time Limitation</span></h2></div><div><span>0</span><span>Total Credits</span></div><div><div><button aria-label=\"Collapse\"><i></i></button></div></div></header><div><div><ul><li data-test=\"ruleView-A\"><div data-test=\"ruleView-A-result\"><div>Most students are expected to complete their Ph.D. program within five years after joining the program. However, students are required to finalize their dissertation within a maximum of seven years after starting the program. This timeline ensures that students remain engaged with their research and maintain a trajectory towards timely graduation, while also providing adequate time to address any challenges that may arise during the dissertation process. Students who do not successfully defend their thesis by the end of the seventh year will be dismissed from the program but may be eligible for an MS degree en route.\n\nIn exceptional cases, students may appeal for an extension to continue the program beyond the seventh year. For more information on UCF’s seven-year rule and the relevant forms, please refer to this link: https://graduate.ucf.edu/7-year-rule-completion-form/\n</div></div></li></ul></div></div></section><h3>Grand Total Credits:<!-- --> <strong>72</strong></h3></div><h1>Application Requirements</h1><h1>Application Deadlines</h1><h1>Financial Information</h1><p>Graduate students may receive financial assistance through fellowships, assistantships, tuition support, or loans. For more information, see the College of Graduate Studies <a href=\"https://funding.graduate.ucf.edu/\" target=\"_blank\">Funding website</a>, which describes the types of financial assistance available at UCF and provides general guidance in planning your graduate finances. The Financial Information section of the Graduate Catalog is another key resource.</p> <p><strong>UCF Student Financial Assistance</strong><br />Millican Hall 120<br />Telephone: 407-823-2827<br />Appointment Line: 407-823-5285<br />Fax: 407-823-5241<br /><a href=\"mailto:finaid@ucf.edu\">finaid@ucf.edu</a><br /><a href=\"http://finaid.ucf.edu/\" target=\"_blank\">Website</a></p><h1>Fellowship Information</h1><p>Fellowships are awarded based on academic merit to highly qualified students. They are paid to students through the Office of Student Financial Assistance, based on instructions provided by the College of Graduate Studies. Fellowships are given to support a student's graduate study and do not have a work obligation. For more information, see <a href=\"https://graduate.ucf.edu/fellowships/\" target=\"_blank\">UCF Graduate Fellowships</a>, which includes descriptions of university fellowships and what you should do to be considered for a fellowship.</p> <p>The department offers over 20 Graduate Teaching Assistantships every year on a competitive basis. A few Graduate Research Assistantships are also available for qualified students.</p> <p><strong>Grad Fellowships</strong><br />Telephone: 407-823-0127<br /><a href=\"mailto:gradfellowship@ucf.edu\">gradfellowship@ucf.edu</a><br /><a href=\"https://funding.graduate.ucf.edu/\" target=\"_blank\">Website</a></p>",
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