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• 18 credit hours must be from APPM at 5000+ level.
• The 18 hours of APPM credits must include 5600 & 5610 (numerics I & II), 5440 & 5450 (analysis I & II), and one more approved \sequence" (see supplement for a list of approved sequences).
• 6 credit hours must be a two-course out-of-department sequence. This sequence needs approval (pre-approval recommended!) from graduate chair. Must be at 5000+ level, and not duplicate material taught by APPM.
• Two 1 credit seminar courses are required. Must be taken after the rst year.
• You must maintain a GPA of 3.0 or better, and earn at least a B- in each class.

Information about preliminary exams is explained in the Supplement on page 8.

Preliminary Examination Rules

• Doctoral students must take and pass two preliminary exams by August at the end of their first year.
• In January, first-year PhD students can take either PDEs or Statistics, depending on the core course they chose to take in their first semester.
• In May, first-year PhD students can choose to take either Applied Analysis or Numerical Analysis, depending on the core course sequence they chose to take in their first year.
• Make-up exams are offered in August.
• You may take any one exam no more than two times.

Tips to Keep in Mind

• Make use of office hours! Digesting necessary content for an exam happens best in a consistent way over time and not during a scramble a few weeks before an exam. If or when you find you have a question that you cannot find an answer for, please attend office hours.
• Plan to meet with the writer of your upcoming prelim exam. The GC created the prelim structure to be transparent in response to student requests. Students can KNOW who will write the exam and can MEET the writers/proctors before (and after) the test to ask questions. Take advantage of this resource, especially setting a plan for checking in with them as you prepare. If you don't see the exam writers posted on your APPM 7400 canvas page, ask the Lead TAs or amgradco@colorado.edu for a list of proctors.
• Make use of exam archives. Test yourself and re-test. Know where your problem areas are and ace them. Simulate a test environment by timing yourself and closing books/notes on a test made of samples from these old exams.
• Email or meet with Grad Reps to see if they are organizing study groups or if they have any advice for you. Senior grad students sometimes organize study sessions ahead of prelims.
• Students are individually responsible for finding time to study on their own or in study groups that they organize or learn of. They should attempt timed mock exams to prepare well.
• Take care of yourself. Keep things calm and consistent in life. Drink. Eat. Exercise. Stay grounded but still focused.
• Preliminary Exam Schedule: Every year, PDE and Statistics Preliminary Exams are held in January, the week before classes start. Analysis and Numerics prelims are held in May, the week preceding Memorial Day. After May prelims, all first-years will be invited to meet with their advisor by June 15^th to go over their first year progress and discuss exam results.  If needed, students can have a final attempt at taking one or both exams in August, the week before classes start.
• If students do not pass both prelims after two attempts, they can discuss options with their advisor in August. A common path for students who don’t pass is to continue to obtain their MS degree at CU and/ or apply for other doctoral programs.

The goal of this document is for students to provide a summary of all the work they have done so far to advance along their research path here including obtaining research training, identifying a research area of interest, and interacting with potential research advisor(s). Students should mention guidance received on advanced course to be taken. The document must also include an indication of how students will use their APPM summer fellowship to enhance their research training. See the "Dissertation Advisor, Faculty Mentor, and Research Plan," section of the Supplement for guidance on activities of interest to discuss. The summary must be signed by an APPM core faculty member relevant to the student's activities and is due April 15th of a PhD student's second year. Questions can be directed to amgradco@colorado.edu or the Graduate Program Chair.

The Graduate Chair will be the advisor for all incoming students.  Once the student has selected an area of specialization and found an Advisor who will take them on, they will inform the Graduate Chair and the Graduate Coordinator.  This usually happens after the students passes their Preliminary Exams and start to focus of their dissertation.

If you are planning on using transfer credits from another accredited University.  Please review this form below and submit the appropriate paperwork.

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The purpose of the comprehensive exam is to ensure that the student has a sufficient grasp of the fundamentals of the chosen thesis area to begin research, the ability to exchange ideas and information with the members of the examining board (thesis committee), and a broad base of knowledge in applied mathematics.

Before the comprehensive exam, the Ph.D. student must submit a 5-10 page thesis proposal, complete with motivation for the topic and references to key papers, to each member of the thesis committee.  This proposal should be written in consultation with the chair of the thesis committee.

The exam will consist of a presentation by the student on his/her research proposal for a maximum of one hour in length, followed by a questioning period of up to one additional hour.  The presentation portion is open to all faculty and students in the program.

Students will need to be registered in classes for the semester they are going to complete their examination for it to count towards that semester. This includes the summer semester.

• Select Committee (see rules on "Thesis Committee" on Page 13 of the Supplement)
• Schedule Comprehensive date and location with committee members. For help reserving rooms, please visit or email amassist@colorado.edu.
• Inform Graduate Coordinator (amgradco@colorado.edu) of your date, location, and member names, and the Graduate Coordinator will help you procure Graduate Faculty Appointments for any out-of-department members when you submit an up-to-date CV to amagradco. (at least 2 weeks prior to Comp date)
• Complete Doctoral Exam Report for committee approval (at least 2 weeks prior to Comp date)
• Submit Title and Abstract to amassist@colorado.edu to post in department (at least 2 weeks prior to Comp date) See example or .tex file
• Complete Candidacy application for an Advanced Degree

Comprehensive Exams are the Year 4 milestone and should be completed by spring or summer of Year 4. Students and their advisors may ask the Grad Program Chair for an extension by email, cc'ing amgradco@colorado.edu. 

The exam will consist of a presentation by the student on his/her research proposal, followed by a questioning period of up to one additional hour.  The presentation portion is open to all faculty and students in the program.

Students will need to be registered in classes for the semester they are going to complete their examination for it to count towards that semester. This includes the summer semester.

• Select Committee (see rules on Exam Report)
• Submit Title of Thesis to Graduate School – see doctoral deadlines for dates
• Complete for committee approval –select Final (at least 3 weeks prior to Defense Date)
  • Get Graduate Chair signature/approval
  • Make copy for Graduate Coordinator
  • Submit original to Graduate School
• Print a copy of Thesis Signature page, get original signatures and submit the form directly to the Graduate School.
• Have Committee Chair pick up Exam Report from Graduate Coordinator prior to Thesis Defense. (Graduate Coordinator will have it ready at least 48 hrs. prior to Exam time)
• Submit Thesis to Graduate School electronically - see doctoral deadlines for dates and instructions.
• Submit 3 hard copies of thesis to Graduate Coordinator. Same due date as Graduate School submission date. This version will serve as the archival copy kept by the University Library. These three copies will be bound for you by the department free of charge (one for you, one for the department, and one for your advisor)
  • One copy must be printed single sided, on 8.5 x 11 watermarked paper of at least 25 % cotton and 20# weight.
  • The other two copies can be printed double sided, on 8.5 x 11 watermarked paper of at least 25 % cotton and 20# weight.
• Submit Thesis to CU Electronic Scholars Depository - see .