2019-2020 Catalog 
    Mar 22, 2023  
2019-2020 Catalog [ARCHIVED CATALOG]

Applied Science, PhD

There are three options in the Applied Science, PhD:

  • Interdisciplinary
  • Mathematics
  • Physics

Interdisciplinary Option

We offer an interdisciplinary option for students who desire a tight integration of two disciplines within the program (Mathematics and Physics). These students will have co-advisors from the two different disciplines. The student and the advisors will design a sequence of courses which is appropriate for the student’s research direction and maintains academic rigor. Because the student in the interdisciplinary option will straddle two disciplines, the student will not be expected to take the full set of qualifying exams for both disciplines. However, the student must take two PhD level qualifying exams from one or both disciplines, demonstrating an appropriate expertise in the selected interdisciplinary areas. For more information regarding this option, please contact Dr. Anatoliy Pinchuk at apinchuk@uccs.edu.

Program Requirements

  • Complete a minimum of 36 credit hours of coursework.
  • Complete a minimum of 30 credit hours of dissertation work. 

Credit hours of coursework and dissertation work must total 75.

Mathematics Option

The Department of Mathematics of the University of Colorado Colorado Springs is delighted to be able to offer a program of study leading to a PhD as part of the University’s PhD in Applied Science degree. For more information on this graduate program, please contact Dr. Chakravarty at schakrav@uccs.edu; 719-255-3549. You can refer to the Math Faculty Research Interests page at http://www.uccs.edu/math/faculty_staff/faculty_research.html for a summary of primary research interests among department faculty. Please see the Math Department website at www.uccs.edu/math/graduate-programs.html for more information.

Admission Requirements

The admission criteria include but are NOT limited to the following requirements. Any decision regarding admission is made by the Graduate Committee on an individual basis, after taking into consideration the application material and supporting documents.

  • Hold a baccalaureate degree from an accredited college or university. Applicants with degrees other than mathematics (e.g., biological sciences, physics, engineering) should have mathematical preparation comparable to that of a baccalaureate in mathematics.
  • Have an undergraduate GPA of at least 3.00 (“A” is equivalent to 4.0).
  • Promising students who do not meet all of the admission requirements may be considered for provisional admission.
  • GRE scores are recommended but not required.

International applicants must demonstrate English language proficiency by one of the approved methods that can be found at: http://www.uccs.edu/math/current-students/graduate/applications_forms.html.

Transfer Credits Policy

Students transferring into the program with graduate work or a Master’s degree in an appropriate discipline must satisfy the admissions requirements above. Graduate level courses completed outside UCCS prior to admission may be transferable into the program. Typically, transfer credits will not exceed 25% of the total required credit hours. In unusual circumstances, applicants may request a review of their records to determine whether additional credits may be transferred. Decisions regarding transfer of graduate credits are made by the appropriate graduate advisor, and are subject to the regulations of the UCCS Graduate School.

Specific Program Requirements

  • Students must satisfy coursework, examination, and dissertation requirements.
  • The total credit hours of graduate coursework and dissertation work applied to the degree must be 75. This total may include coursework applied toward a Master’s degree.
  • Students must complete a minimum of 30 credit hours of graduate coursework, and a minimum of 30 credit hours of dissertation work.
  • Independent study may not exceed 25% of the minimum number of credit hours required for the degree.
  • As part of the graduate coursework, students must complete 3 two-semester sequences from the list of core courses.

Mathematics Core Courses (18 credit hours)

Each PhD student in the mathematics track will complete three designated course sequences chosen from the following areas. They will choose two sequences on which to complete departmental exams.


  • Students in the PhD program will normally take two written preliminary examinations and two written comprehensive examinations.
  • These examinations are closely linked to the content of graduate courses, but they have distinct content descriptions, and may require independent study of material not covered in the courses.
  • The preliminary examinations cover real analysis and linear algebra at the Master’s degree level. The graduate committee will review the performance on the preliminary examinations to determine if the student may move forward in the PhD program. At the discretion of the graduate committee, the required preliminary examinations may be waived for students entering the graduate program with a Master’s degree, or with a comparable level of preparation.
  • The two PhD comprehensive examinations will each cover material corresponding to one of the three required PhD core sequences.
  • Normally, students will have at most two attempts to pass each comprehensive exam, and may attempt exams in no more than three distinct core subject areas. Exceptions must be approved by the graduate committee.
  • There will be an oral dissertation proposal examination administered by the dissertation advisory committee to determine if the dissertation topic is appropriate, and if the student is adequately prepared for work on the dissertation.
  • After the dissertation has been accepted by the dissertation advisor, a final oral dissertation defense examination will be conducted by the dissertation advisory committee.

Physics Option

The Physics Department offers a program leading to a PhD in Applied Science with a specialization in Physics. The key information about the program is given below.

For information about the graduate program, please contact Prof. Anatoliy Pinchuk at apinchuk@uccs.edu.

The primary research interests of the department can be found at http://www.uccs.edu/~physics/research.html.

Admission Requirements

All applicants must, at a minimum, meet the following requirements for regular admission:

  •  Hold a baccalaureate degree in biological sciences, mathematics, physics or equivalents from an accredited college or university and have an appropriate background of undergraduate physics courses.
  •  Have an undergraduate GPA of at least 3.00 (“A” is equivalent to 4.0).
  •  Submit 1 Official Transcript of all previous graduate and undergraduate work.
  •  Provide three letters of recommendation, all past university transcripts and fill out an application form.
  •  Submit a 1-2 page goal statement.
  •  Have interests that fit with the department’s research directions.

Graduate application forms can be found on the Graduate School website.

Promising students who do not meet all of the requirements may be considered as provisional applicants. Provisional status may be removed when the student fulfills all the requirements set out by the Physics Department when they were admitted. Students admitted provisionally should work with the Physics graduate adviser to ensure they have all the coursework preparation needed before undertaking graduate-level classes.


Additional requirements for some students

  • Students with international transcripts must take the Physics GRE exam. A minimum score for regular admission is in the range of 520-550.
  • Applicants for whom English is a second language must complete the TOEFL exam with a minimum score of 560 (paper-based exam) or 83 (internet-based exam) or 220 (internet-based exam). A band score of 6.5 on the IELTS is also acceptable. If the student has successfully completed one year of full-time academic study at a U.S. institution, this requirement can be waived. An oral interview with Physics faculty may also be required as proof of English proficiency, as the department sees fit.
  • Applicants who already hold a Masters degree in Physics should discuss their application with a potential faculty research adviser in advance, and mention these discussions in their goal statement.

Transfer of Credits

Students transferring into the program with a Master’s degree in an appropriate discipline also need to satisfy all the standards below for graduation. However, students may request a review of their existing credits and may have the number of credits required reduced at the discretion of the physics graduate advisor. If appropriate, the entire set of Master’s degree courses can be applied to the PhD program.

Program Requirements

The student must complete a total of 66 credit hours of coursework and dissertation. This includes:

    1. A minimum of 36 credit hours of coursework with GPA above 3.0:

  • 21 credit hours of Core courses
  • 15 credit hours of Specialization, Elective or Interdisciplinary courses

    2. A minimum of 30 credit hours of dissertation work, and complete and successfully defend the dissertation.

By the time students have successfully completed the coursework requirements of the PhD program, they must identify a dissertation adviser who agrees to supervise their research work. Students should enroll in dissertation hours with their adviser and to do so should ask the Physics Program Assistant for an enrollment code. Students who do not identify a willing dissertation adviser must exit the program.


There will be a comprehensive examination administered by the dissertation advisory committee to determine if the dissertation topic is appropriate, and if the student is adequately prepared for work on the dissertation. This exam will normally be given when a student has completed 9 dissertation credit hours. Students refusing to take the comprehensive exam when asked by Physics faculty member(s) may have a hold placed on their enrollment until this fulfilment is completed.

After the dissertation has been accepted by the dissertation advisor, a final oral dissertation defense examination will be conducted by the dissertation advisory committee. The dissertation committee will contain four physics faculty plus one outside member of the graduate faculty (from another department or another university). The dissertation advisor will be in charge of choosing the committee.