phd in mathematics usa

PhD Program

During their first year in the program, students typically engage in coursework and seminars which prepare them for the  Qualifying Examinations .  Currently, these two exams test the student’s breadth of knowledge in algebra and real analysis. Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics.

Current Course Requirements: To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297.

Within the 27 units, students must satisfactorily complete a course sequence. This can be fulfilled in one of the following ways:

Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry

• Math 216A, B, & C: Introduction to Algebraic Geometry
• Math 230A, B, & C: Theory of Probability
• 3 quarter course sequence in a single subject approved in advance by the Director of Graduate Studies.

Course Requirements for students starting in Autumn 2023 and later: 

To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297. (The course sequence requirement is discontinued for students starting in Autumn 2023 and later.)

By the end of Spring Quarter of their second year in the program, students must have a dissertation advisor and apply for Candidacy.

During their third year, students will take their Area Examination, which must be completed by the end of Winter Quarter. This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also used as an opportunity for the student to present their committee with a summary of research conducted to date as well as a detailed plan for the remaining research.

Typically during the latter part of the fourth or early part of the fifth year of study, students are expected to finish their dissertation research. At this time, students defend their dissertation as they sit for their University Oral Examination. Following the dissertation defense, students take a short time to make final revisions to their actual papers and submit the dissertation to their reading committee for final approval.

All students continue through each year of the program serving some form of Assistantship: Course, Teaching or Research, unless they have funding from outside the department.

Our graduate students are very active as both leaders and participants in seminars and colloquia in their chosen areas of interest.

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Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

• The firm deadline for applications for Autumn 2024, is December 4, 2023.
• The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

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Ph.D. Program Overview

Description.

The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to six years of graduate study to complete. One feature that makes the program at Cornell particularly attractive is the broad range of  interests of the faculty . The department has outstanding groups in the areas of algebra, algebraic geometry,  analysis, applied mathematics, combinatorics, dynamical systems, geometry, logic, Lie groups, number theory, probability, and topology. The field also maintains close ties with distinguished graduate programs in the fields of  applied mathematics ,  computer science ,  operations research , and  statistics .

Core Courses

A normal course load for a beginning graduate student is three courses per term. 

There are no qualifying exams, but the program requires that all students pass four courses to be selected from the six core courses. First-year students are allowed to place out of some (possibly, all) of the core courses. In order to place out of a course, students should contact the faculty member who is teaching the course during the current academic year, and that faculty member will make a decision. The minimum passing grade for the core courses is B-; no grade is assigned for placing out of a core course.

At least two core courses should be taken (or placed out) by the end of the first year. At least four core courses should be taken (or placed out) by the end of the second year (cumulative). These time requirements can be waived for students with health problems or other significant non-academic problems. They can be also waived for students who take time-consuming courses in another area (for example, CS) and who have strong support from a faculty; requests from such students should be made before the beginning of the spring semester. 

The core courses  are distributed among three main areas: analysis, algebra and topology/geometry. A student must pass at least one course from each group. All entering graduate students are encouraged to eventually take all six core courses with the option of an S/U grade for two of them. 

The six core courses are:

MATH 6110, Real Analysis

MATH 6120, Complex Analysis

MATH 6310, Algebra 1

MATH 6320, Algebra 2

MATH 6510, Introductory Algebraic Topology

MATH 6520, Differentiable Manifolds.

Students who are not ready to take some of the core courses may take MATH 4130-4140, Introduction to Analysis, and/or MATH 4330-4340, Introduction to Algebra, which are the honors versions of our core undergraduate courses.

"What is...?" Seminar

The "What Is...?" Seminar is a series of talks given by faculty in the graduate field of Mathematics. Speakers are selected by an organizing committee of graduate students. The goal of the seminar is to aid students in finding advisors.

Schedule for the "What Is...?" seminar

Special Committee

The Cornell Graduate School requires that every student selects a special committee (in particular, a thesis adviser, who is the chair or the committee) by the end of the third semester.

The emphasis in the Graduate School at Cornell is on individualized instruction and training for independent investigation. There are very few formal requirements and each student develops a program in conjunction with his or her special committee, which consists of three faculty members, some of which may be chosen from outside the field of mathematics. 

Entering students are not assigned special committees. Such students may contact any of the members on the Advising Committee if they have questions or need advice.

Current Advising Committee

Analysis / Probability / Dynamical Systems / Logic: Lionel Levine Geometry / Topology / Combinatorics: Kathryn Mann Probability / Statistics:  Philippe Sosoe Applied Mathematics Liaison: Richard Rand

Admission to Candidacy

To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student's fourth year. Upon passing the A exam, the student will be awarded (at his/her request) an M.S. degree without thesis.

The admission to candidacy examination is given to determine if the student is “ready to begin work on a thesis.” The content and methods of examination are agreed on by the student and his/her special committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, he/she must demonstrate expertise beyond just mastery of basic mathematics covered in the core graduate courses. 

To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the special committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes five to six years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the special committee. By the time of the oral admission to candidacy examination, the candidate should have selected as chairperson of the committee the faculty member who will supervise the research. When the thesis is completed, the student presents his/her results at the thesis defense or B Exam. All doctoral students take a Final Examination (the B Exam, which is the oral defense of the dissertation) upon completion of all requirements for the degree, no earlier than one month before completion of the minimum registration requirement.

Masters Degree in the Minor Field

Ph.D. students in the field of mathematics may earn a Special Master's of Science in Computer Science. Interested students must apply to the Graduate School using a form available for this purpose. To be eligible for this degree, the student must have a member representing the minor field on the special committee and pass the A-exam in the major field. The rules and the specific requirements for each master's program are explained on the referenced page.

Cornell will award at most one master's degree to any student. In particular, a student awarded a master's degree in a minor field will not be eligible for a master's degree in the major field.

Graduate Student Funding

Funding commitments made at the time of admission to the Ph.D. program are typically for a period of five years. Support in the sixth year is available by application, as needed. Support in the seventh year is only available by request from an advisor, and dependent on the availability of teaching lines. Following a policy from the Cornell Graduate School, students who require more than seven years to complete their degree shall not be funded as teaching assistants after the 14th semester.

Special Requests

Students who have special requests should first discuss them with their Ph.D. advisor (or with a field member with whom they work, if they don't have an advisor yet). If the advisor (or field faculty) supports the request, then it should be sent to the Director of Graduate Studies.  

PhD in Mathematics

The PhD in Mathematics consists of preliminary coursework and study, qualifying exams, a candidacy exam with an adviser, and creative research culminating in a written dissertation and defense. All doctoral students must also do some teaching on the way to the PhD. There are minimal course requirements, and detailed requirements and procedures for the PhD program are outlined in the  PhD Handbook .

Please note that our department alternates recruiting in-coming classes that are focused on either applied or pure mathematics. For the Fall 2024 admissions (matriculation in September 2024), we are focusing on students interested in areas of applied mathematics.

All our professors are active in research, and are devoted to teaching and mentoring of students. Thus, there are many opportunities to be involved in cutting-edge research in pure and applied mathematics. Moreover, the seven other research universities in the Boston area are all within easy reach, providing access to many more classes, seminars and colloquia in diverse areas of mathematical research.

Teaching assistantships are available for incoming PhD students, as well as a limited number of University-wide fellowships. Tufts has on-campus housing for graduate students, but many choose to live off-campus instead.

In addition to the above, PhD students often:

• Mentor undergraduates as teaching assistants and course instructors, and through graduate-student run programs like the Directed Reading Program.
• Meet with advisors and fellow students to share research and collaborate with scholars across disciplines
• Attend professional development workshops and present research at conferences

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Georgia Institute of Technology College of Sciences

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PhD in Mathematics

Here are the requirements for earning the PhD degree in Mathematics offered by the School of Math. For requirements of other PhD programs housed within the School, please see their specific pages at  Doctoral Programs . The requirements for all these programs consist of three components:  coursework ,  examinations , and  dissertation  in accordance to the guidelines described in the  GT Catalogue .

Completion of required coursework, examinations, and dissertation normally takes about five years. During the first one or two years, students concentrate on coursework to acquire the background necessary for the comprehensive examinations. By the end of their third year in the program, all students are expected to have chosen a thesis topic, and begin work on the research and writing of the dissertation.

The program of study must contain at least 30 hours of graduate-level coursework (6000-level or above) in mathematics and an additional 9 hours of coursework towards a minor. The minor requirement consists of graduate or advanced undergraduate coursework taken entirely outside the School of Mathematics, or in an area of mathematics sufficiently far from the students area of specialization.

Prior to admission to candidacy for the doctoral degree, each student must satisfy the School's comprehensive examinations (comps) requirement. The first phase is a written examination which students must complete by the end of their second year in the graduate program. The second phase is an oral examination in the student's proposed area of specialization, which must be completed by the end of the third year.

Research and the writing of the dissertation represent the final phase of the student's doctoral study, and must be completed within seven years of the passing of comps. A final oral examination on the dissertation (theses defense) must be passed prior to the granting of the degree.

The Coursework

The program of study must satisfy the following  hours ,  minor , and  breadth  requirements. Students who entered before Fall 2015 should see  the old requirements , though they may opt into the current rules described below, and are advised to do so.

Hours requirements.  The students must complete 39 hours of coursework as follows:

• At least 30 hours must be in mathematics courses at the 6000-level or higher.
• At least 9 hours must form the doctoral minor field of study.
• The overall GPA for these courses must be at least 3.0.
• These courses must be taken for a letter grade and passed with a grade of at least C.

Minor requirement.  The minor field of study should consist primarily of 6000-level (or higher) coursework in a specific area outside the School of Math, or in a mathematical subject sufficiently far from the student’s thesis work. A total of 9 credit hours is required and must be passed with a grade of B or better. These courses should not include MATH 8900, and must be chosen in consultation with the PhD advisor and the Director of Graduate Studies to ensure that they form a cohesive group which best complements the students research and career goals. A student wishing to satisfy the minor requirement by mathematics courses must petition the Graduate Committee for approval.  Courses used to fulfill a Basic Understanding breadth requirement in Analysis or Algebra should not be counted towards the doctoral minor. Upon completing the minor requirement, a student should immediately complete the  Doctoral Minor form .

Breadth requirements.  The students must demonstrate:

• Basic understanding of 2 subjects must be demonstrated through passing the subjects' written comprehensive exams.  At least 1 of these 2 exams must be in Algebra or Analysis.
• Basic understanding of the third subject may be demonstrated either by completing two courses in the subject (with a grade of A or B in each course) or by passing the subject's written comprehensive exam.
• A basic understanding of both subjects in Area I (analysis and algebra) must be demonstrated.
• Earning a grade of A or B in a one-semester graduate course in a subject demonstrates exposure to the subject.
• Passing a subject's written comprehensive exam also demonstrates exposure to that subject.

The subjects.  The specific subjects, and associated courses, which can be used to satisfy the breadth requirements are as follows.

• Area I subjects:​
• Area II subjects:​

Special Topics and Reading Courses.

• Special topics courses may always be used to meet hours requirements.
• Special topics courses may be used to meet breadth requirements, subject to the discretion of the Director of Graduate Studies.
• Reading courses may be used to meet hours requirements but not breadth requirements.

Credit Transfers

Graduate courses completed at other universities may be counted towards breadth and hours requirements (courses designated as undergraduate or Bachelors' level courses are not eligible to transfer for graduate credit).  These courses do not need to be officially transferred to Georgia Tech. At a student’s request, the Director of Graduate Studies will determine which breadth and hours requirements have been satisfied by graduate-level coursework at another institution.  

Courses taken at other institutions may also be counted toward the minor requirement, subject to the approval of the Graduate Director; however, these courses must be officially transferred to Georgia Tech.

There is no limit for the transfer of credits applied toward the breadth requirements; however, a maximum of 12 hours of coursework from other institutions may be used to satisfy hours requirements. Thus at least 27 hours of coursework must be completed at Georgia Tech, including at least 18 hours of 6000-level (or higher) mathematics coursework.

Students wishing to petition for transfer of credit from previous graduate level work should send the transcripts and syllabi of these courses, together with a list of the corresponding courses in the School of Math, to the Director of Advising and Assessment for the graduate program.

Comprehensive Examinations

The comprehensive examination is in two phases. The first phase consists of passing two out of seven written examinations. The second phase is an oral specialty examination in the student's planned area of concentration. Generally, a student is expected to have studied the intended area of research but not necessarily begun dissertation research at the time of the oral examination.

Written examinations.  The written examinations will be administered twice each year, shortly after the beginning of the Fall and Spring semesters. The result of the written examination is either pass or fail. For syllabi and sample exams see the  written exams page .

All students must adhere to the following rules and timetables, which may be extended by the Director of Graduate Studies, but only at the time of matriculation and only when certified in writing. Modifications because of leaves from the program will be decided on a case-by-case basis.

After acceptance into the PhD Program in Mathematics, a student must pass the written examinations no later than their fourth administration since the student's doctoral enrollment. The students can pass each of the two written comprehensive exams in separate semesters, and are allowed multiple attempts.

The Director of Graduate Studies (DGS) will be responsible for advising each new student at matriculation of these rules and procedures and the appropriate timetable for the written portion of the examination. The DGS will also be responsible for maintaining a study guide and list of recommended texts, as well as a file of previous examinations, to be used by students preparing for this written examination.

Oral examination.  A student must pass the oral specialty examination within three years since first enrolling in the PhD program, and after having passed the written portion of the comprehensive exams. The examination will be given by a committee consisting of the student's dissertation advisor or probable advisor, two faculty members chosen by the advisor in consultation with the student, and a fourth member appointed by the School's Graduate Director. The scope of the examination will be determined by the advisor and will be approved by the graduate coordinator. The examining committee shall either (1) pass the student or (2) fail the student. Within the time constraints of which above, the oral specialty examination may be attempted multiple times, though not more than twice in any given semester. For more details and specific rules and policies see the  oral exam page .

Dissertation and Defense

A dissertation and a final oral examination are required. For details see our  Dissertation and Graduation  page, which applies to all PhD programs in the School of Math.

Graduate Program

Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we urge independent work and research, there exists a real sense of camaraderie among our graduate students. As a result, the atmosphere created is one of excitement and stimulation as well as of mentoring and support. Furthermore, there exists a strong scholarly relationship between the Math Department and the Institute for Advanced Study, located just a short distance from campus, where students can make contact with members there as well as attend the IAS seminar series.  Our program has minimal requirements and maximal research and educational opportunities. We offer a broad variety of advanced research topics courses as well as more introductory level courses in algebra, analysis, and geometry, which help first-year students strengthen their mathematical background and get involved with faculty through basic course work. In addition to the courses, there are several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the Department Colloquium give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students for graduate students, creating a vibrant mathematical interaction among them; and, (3) What’s Happening in Fine Hall (WHIFH) seminar where faculty give talks in their own research areas specifically geared towards graduate students. Working or reading seminars in various research fields are also organized by graduate students each semester. First-year students are set on the fast track of research by choosing two advanced topics of research, beyond having a strong knowledge of three more general subjects: algebra, and real and complex analysis, as part of the required General Examination. It is the hope that one, or both, of the advanced topics will lead to the further discovery of a thesis problem. Students are expected to write a thesis in four years but will be provided an additional year to complete their work if deemed necessary. Most of our Ph.D.'s are successfully launched into academic positions at premier mathematical institutions as well as in industry .

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Ph.D. Program

Introduction.

These guidelines are intended to help familiarize graduate students with the policies governing the graduate program leading to the degrees of Doctor of Philosophy (Ph.D.) in Applied Mathematics. This material supplements the graduate school requirements found on the  Graduate Student Resources  page and the  Doctoral Degree Policies  of the graduate school. Students are expected to be familiar with these procedures and regulations.

The Doctor of Philosophy program

The Doctor of Philosophy (Ph.D.) Degree in Applied Mathematics is primarily a research degree, and is not conferred as a result of course work. The granting of the degree is based on proficiency in Applied Mathematics, and the ability to carry out an independent investigation as demonstrated by the completion of a doctoral dissertation. This dissertation must exhibit original mathematical contributions that are relevant to a significant area of application.

Course requirements for the Ph.D. program

• AMATH 561, 562, 563
• AMATH 567, 568, 569
• AMATH 584, 585, 586
• AMATH 600: two, 2-credit readings, each with a different faculty member, to be completed prior to the start of the student's second year.
• Students must take a minimum of 15 numerically graded courses. At most two of these can be at the 400 level or be cross listed with courses at the 400 level. Graduate level courses previously taken at UW (e.g., during a Master's program) count toward this requirement. Graduate level courses taken outside of UW may count toward the requirement for 15 numerically graded courses with the approval of the Graduate Program Coordinator. The entire course of study of a student and all exceptions to this list must be approved by the Graduate Program Coordinator and the student’s advisor or faculty mentors.

For students who entered the doctoral program autumn 2017 or autumn 2018, please see these degree requirements. For students who entered the doctoral program prior to autumn 2017, please see these degree requirements.  

Faculty mentoring

Upon arrival, incoming students will be assigned two faculty mentors. Until a student settles on an advisor, the faculty mentors aid the student in selecting courses, and they each guide the student through a 2-credit independent reading course on material related to the student’s research interest. The faculty mentors are not necessarily faculty in the Department of Applied Mathematics.

Faculty advisor

By the end of a student’s first summer quarter, an advisor must be determined.  T he advisor provides guidance in designing a course of study appropriate for the student’s research interests, and in formulating a dissertation topic.

A full Supervisory Committee should be formed four months prior to the student’s General Exam. The full Supervisory Committee should have a minimum of three regular members plus the Graduate School Representative , and will consist of at least two faculty members from Applied Mathematics, one of whom is to be the Chair of the Committee. If the proposed dissertation advisor is a member of the Applied Mathematics faculty, then the advisor will be the Chair. The dissertation advisor may be from another department,  or may have an  affiliate  (assistant, associate, full) professor appointment with the Applied Mathematics department  and is then also a member of the Supervisory Committee.

The Dissertation Reading Committee , formed after the General Exam,  is a subset of  at least   three members from the Supervisory Committee   who are appointed to read and approve the dissertation.  Two members of the Dissertation Reading Committee must be from the Applied Mathematics faculty. At least one of the committee members must be a member of the core  Applied Mathematics faculty. It is required that this member is present for both the general and final examination, and is included on the reading committee.

While the principal source of guidance during the process of choosing specialization areas and a research topic is the thesis advisor, it is strongly advised that the student maintain contact with all members of the Supervisory Committee. It is suggested that the student meet with the Supervisory Committee at least once a year to discuss their progress until the doctoral thesis is completed.

Examination requirements for the Ph.D. program

Students in the Ph.D. program must pass the following exams:

• The  qualifying exam
• The  general exam
• The  final exam  (defense)

Satisfactory performance and progress

At all times, students need to make satisfactory progress towards finishing their degree. Satisfactory progress in course work is based on grades. Students are expected to maintain a grade point average of 3.4/4.0 or better. Satisfactory progress on the examination requirements consists of passing the different exams in a timely manner. Departmental funding is contingent on satisfactory progress.   The Graduate School rules regarding satisfactory progress are detailed in Policy 3.7: Academic Performance and Progress .   The Department of Applied Mathematics follows these recommended guidelines of the Graduate School including an initial warning, followed by a maximum of three quarters of probation and one quarter of final probation, then ultimately being dropped from the program.    We encourage all students to explore and utilize the many available  resources  across campus.

Expected academic workload

A first-year, full-time student is expected to register for a full course load, at least three numerically graded courses, typically totaling 12-18 credits. All other students are expected to consult with their advisor and register for at least 10-18 credits per quarter.  Students who do not intend to register for a quarter must seek approved  academic leave  in order to maintain a student status.   Students who do not maintain active student status through course registration or an approved leave request need to request reinstatement to rejoin the program. Reinstatement is at the discretion of the department. Students approved for reinstatement are required to follow degree requirements active at time of reinstatement. 

Annual Progress Report

Students are required to submit an Annual Progress Report to the Graduate Program Coordinator by the second week of Spring Quarter each year. The annual progress report should contain the professional information related to the student’s progress since the previous annual report. It should contain information on courses taken, presentations given, publications, thesis progress, etc., and should be discussed with the student's advisor prior to submission. Students should regard the Annual Progress Report as an opportunity to self-evaluate their progress towards completing the PhD. The content of the Annual Progress Report is used to ensure the student is making satisfactory progress towards the PhD degree.

Financial assistance

Financial support for Doctoral studies is limited to five years after admission to the Ph.D. program in the Department of Applied Mathematics. Support for an additional period may be granted upon approval of a petition, endorsed by the student’s thesis supervisor, to the Graduate Program Coordinator.

Master of Science program

Students in the Ph.D. program obtain an M.Sc. Degree while working towards their Ph.D. degree by satisfying the  requirements for the M.Sc. degree.  

Additional Ph.D. Degree Options and Certificates

Students in the Applied Mathematics Ph.D. program are eligible to pursue additional degree options or certificates, such as the  Advanced Data Science Option  or the  Computational Molecular Biology Certificate .  Students must be admitted and matriculated to the PhD program prior to applying for these options. Option or certificate requirements are in addition to the Applied Mathematics degree requirements. Successful completion of the requirements for the option or the certificate leads to official recognition of this fact on the UW transcript.

Career resources, as well as a look at student pathways after graduation, may be found   here.

FAQs |  Contact the Graduate Program  |  Apply Now

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Doctor of Philosophy in Applied and Industrial Mathematics  Unit: College of Arts and Sciences (GA) Department: Mathematics    Program Website   Academic Plan Code(s): MATHPHD

Program Information

The University of Louisville Department of Mathematics is a research-oriented department that prides itself on delivering first-rate graduate instruction. There are a broad range of courses and ample opportunities to interact with faculty. The Department also maintains an active colloquium series with talks given by visiting mathematicians, statisticians and scientists.

The PhD program in Applied and Industrial Mathematics offers a blend of advanced mathematical and statistical knowledge with the experience to apply that knowledge. Students completing the program have a unique perspective from which they can see the whole of mathematics integrated with applied and industrial needs. A broad and rigorous mathematical core combined with customized application electives and an industrial internship prepares students with life-long career skills in teaching, research, and industry.

Prerequisites

Undergraduate coursework equivalent to a major in mathematics from an accredited university. This should include at least a one-year course in either analysis or abstract algebra, equivalent to MATH 501 - MATH 502 and MATH 521 - MATH 522  at the University of Louisville.

Candidates who have not taken both must complete the second in their program.

Dual Degree Program in Applied and Industrial Mathematics (PhD) and Biostatistics (MS)

Dual degrees in Biostatistics and Applied and Industrial Mathematics are offered by the College of Arts and Sciences and the School of Public Health and Information Sciences. Upon completion of the program, students will receive a PhD in Applied and Industrial Mathematics and a Master of Science in Biostatistics.

Admission Requirements

Interested applicants should have completed undergraduate coursework equivalent to a major in mathematics from an accredited university. This should include at least a one-year course in either analysis or abstract algebra, equivalent to  MATH 501 - MATH 502  and  MATH 521 - MATH 522  at the University of Louisville.

Candidates who have not taken both sequences must complete the second in their program.

Prospective students can apply online . Complete applications require the following:

• Graduate Application form along with paid application fee
• Cover letter to Mathematics department including any information you believe will help process your application. Please indicate in this letter whether you are interested in a GTA position, for example
• Transcripts (an official copy for each undergraduate institution attended. University of Louisville transcripts are automatically submitted)
• At least two letters of recommendation 
• Recent (within three years) GRE scores (only the general exam is required)
• All applicants for whom English is a second language must also submit official TOEFL scores of 79 or higher on the internet-based test, 213 or higher on the computer-based test. English proficiency can also be met by submitting official IELTS scores of at least 6.5 overall band score from the academic module exam or official Duolingo overall score of 105.  Students holding a bachelor's or advanced degree from an accredited institution in the United States may be exempt from this requirement.

For full consideration please submit complete applications by:

Spring admission deadline: November 1 Fall admission deadline: March 1

Late applications will be considered.

Dual Degree Program in Applied and Industrial Mathematics and Biostatistics  Application Procedure

To be admitted to the program, the student is required to apply to and be accepted by both the Department of Mathematics and the Department of Bioinformatics and Biostatistics. A student seeking admission into this program must submit letters to both the Department of Mathematics and the Department of Bioinformatics and Biostatistics stating the intent to take advantage of the dual degree program, as well as their choice of the thesis or non-thesis option for the MS in Biostatistics. Students must submit two recent letters of recommendation with their letter of intent. Applicants will receive written notification stating whether their admission request has been approved or disapproved.

Students currently enrolled in the PhD in Applied and Industrial Mathematics program will need to submit complete application materials to the Department of Bioinformatics and Biostatistics for admission to the MS component of the dual degree, as well as notify his/her advisor in the Department of Mathematics of the intention to enter into the dual degree program. Letters of recommendation for admission to the MS program can be taken from the letters of recommendation written for admission to the PhD program, provided they have been written sufficiently recently.

Program Requirements

Doctor of philosophy in applied and industrial mathematics.

All students admitted to the program must complete the following coursework (or their approved equivalent) and other degree requirements:

Additional Topics and Area of Specialization

In addition to the core, an application area of 18 credit hours will be required. The courses may be in a department outside Mathematics. They will be chosen in consultation with the student's advisory committee.

Qualifying Examinations

Students must pass three written examinations. Two of these will be chosen from the areas of Algebra, Combinatorics and Real Analysis. The third will be chosen from the areas of Mathematical Modeling, Mathematical Statistics and Probability. Normally, these will be taken within a year of completion of the core coursework. These examinations need not be taken together and each may be attempted at most twice.

Industrial Internship

Each student, with prior approval of the Graduate Studies Director, has to complete an internship in an appropriate industrial or governmental setting, or have equivalent experience.

Computing Project

Each student must complete an approved computer project related to the student's area of concentration.

Candidacy Examination

Each student must pass an oral examination in the chosen area of concentration. Usually, at most two attempts at passing this examination will be permitted. Students who wish to make a third attempt must petition the Graduate Studies Committee of the department for permissions to do so.

Dissertation

12 to 18 credit hours: A doctoral dissertation is required of each student.

Required Courses

The required courses for the dual degree program consist of all non-overlapping core courses for both the PhD in Applied and Industrial Mathematics, as well as the course requirements for the MS in Biostatistics. Courses taken to satisfy the Biostatistics component of the dual degree program can be applied to these 18 credit hours of electives which are required for the PhD in Applied and Industrial Mathematics.

Students currently enrolled in the PhD in Applied and Industrial Mathematics program will need to submit complete application materials to the Department of Bioinformatics and Biostatistics for admission to the MS component of the dual degree, as well as notify his/her advisor in the Department of Mathematics of the intention to enter into the dual degree program (see Admissions tab).

Requirements for the PhD in Applied and Industrial Mathematics

Elective/application area courses.

18 credit hours of  Application Area courses are chosen in consultation with a student's advisory committee. These courses can be outside of the Department of Mathematics. C ourses taken to satisfy the Biostatistics component of the dual degree program can be approved to satisfy these 18 credit hours.

Each student, with prior approval of the Graduate Studies Director and the Industrial Internship Director, has to complete an internship in an appropriate industrial or governmental setting, or have equivalent experience.  The Industrial Internship required by the Department of Mathematics and the Master's Project or Thesis required for the MS can be satisfied by a single internship and technical report which simultaneously satisfies the requirements for both degrees. Specifically, the internship must both focus on biostatistics so that it satisfies the Project or Thesis, and contain advanced mathematical content so that it satisfies the Industrial Internship. Likewise, the technical report must meet two requirements: it must satisfy the requirements for a Master's Project report or Master's Thesis for the MS degree and it must be written at an advanced mathematical level expected Industrial Internship. Students should enroll in the Master's Project ( PHST 675 ) or Master's Thesis ( PHST 666 ) courses during or shortly after completion of the Industrial Internship to take advantage of the combined Industrial Internship and Master's Project/Thesis.

Dual-degree students will not be permitted to enroll in the Master's Project ( PHST 675 ) or Master's Thesis ( PHST 666 ) courses until at least two qualifying examinations toward the PhD in Applied and Industrial Mathematics have been completed.

Other Requirements

Students must pass qualifying examinations, complete an approved computing project, and pass a candidacy examination as detailed in the catalog entry for the PhD in Applied and Industrial Mathematics.

In order for the student to fulfill the PhD requirements, the student must satisfy both the qualifying examination and dissertation requirements (12-18 credit hours)  for the PhD in Applied and Industrial Mathematics. Failure to complete these requirements will not jeopardize the MS degree if all its requirements have been satisfactorily completed.

MS in Biostatistics

The PHST 661 - PHST 662 / MATH 561 - MATH 562 requirement is waived if the student takes MATH 663 and MATH 667 . The PHST 681 - PHST 682 requirement is waived if the student takes MATH 667 - MATH 668 . Both requirements ( PHST 661 - PHST 662 / MATH 561 - MATH 562 and PHST 681 - PHST 682 ) are waived only if the student completes both the MATH 663 - MATH 664 and MATH 667 - MATH 668 sequences.

Courses taken to satisfy the Biostatistics component of the dual degree program can be applied to the 18 credit hours of electives which are required for the PhD in Applied and Industrial Mathematics.

A course in public health is a requirement for any student graduating with the MS degree from the Department of Bioinformatics and Biostatistics. These credit hours are not applied to the MS degree.

Electives are chosen in consultation with an advisor, typically from PHST 603 , PHST 620 , PHST 640 , PHST 675 , and PHST 682 .

To be completed in accordance with the guidelines written in the catalog entry for the MS in Bioinformatics and Biostatistics Degree.

Combined Industrial Internship, Practicum and Master's Thesis [six - eight (6-8) credit hours]

Special considerations: students who have already completed a master's degree in the department of mathematics.

To preserve the spirit of a dual degree, such students need to complete 36 credit hours of courses as required for the MS in Biostatistics. Six (6) credit hours of the previous master's degree coursework can be applied to this requirement. The remaining credit hours must be chosen from the list of not covered by core courses approved electives for the Department of Bioinformatics and Biostatistics, with preference given to courses in the Departments of Mathematics and Bioinformatics and Biostatistics. Combined Industrial Internship, Practicum and Master's Thesis cannot be replaced by a previous master's thesis. This requirement must be satisfied as previously described, meeting the specifications of both departments.

The University of Louisville is committed to and will provide equality of educational and employment opportunity for all persons regardless of race, sex, age, color, national origin, ethnicity, creed, religion, disability, genetic information, sexual orientation, gender, gender identity and expression, marital status, pregnancy or veteran status.

Every effort has been made to make the catalog accurate as of the date of publication. However, the University of Louisville reserves the right to change programs of study, academic policies, academic requirements, fees, course information, procedures for the confirmation of degrees, or the announced academic calendar and related deadlines without prior notice. Copyright © 2023-2024, University of Louisville. All rights reserved.

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PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

• Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
• Analysis (examples include MA 711, MA 713, and MA 717)
• PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
• Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
• Topology (examples include MA 721, MA 722, and MA 727)
• Geometry (examples include MA 725, MA 731, and MA 745)
• Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
• Applied Mathematics (examples include MA 750, MA 751, and MA 770)
• Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
• Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
• Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

More Information

Please reach out to us directly at [email protected] if you have further questions.

Department of Mathematics

Requirements for the ph.d. degree.

In order to qualify for the Mathematics Ph.D., all students are required to:

• Complete eight term courses at the graduate level, at least two with Honors grades.
• Pass qualifying examinations on their general mathematical knowledge;
• Submit a dissertation prospectus;
• Participate in the instruction of undergraduates ;
• Be in residence for at least three years;
• Complete a dissertation that clearly advances understanding of the subject it considers.

All students must also complete any other  Graduate School of Arts and Sciences degree requirements  as they appear in the Programs and Policies bulletin.

The normal time for completion of the Ph.D. program is five to six years. Requirement (1) normally includes basic courses in algebra, analysis, and topology.  Students typically complete the eight-course requirement by the end of their third year.  The Honors grades of (1) must be achieved within the first two years.  A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term.  All qualifying examinations must be passed by the end of the second year.  There is no limit to the number of times that students can take the exams, and so they are encouraged to take them as soon as possible.

The dissertation prospectus should be submitted during the third year. 

The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)–(5) and obtaining an adviser.

In addition to all other requirements, students must successfully complete MATH 991a, Ethical Conduct of Research, prior to the end of their first year of study. This requirement must be met prior to registering for a second year of study.

Master’s Degrees :

The M.Phil. and M.S. degrees are conferred only en route to the Ph.D.; there is no separate master’s program in Mathematics.

M.Phil.   Please refer to the Graduate School Degree Requirements

M.S.   A student must complete six term courses with at least one Honors grade, perform adequately on the general qualifying examination, and be in residence at least one year.

Doctor of Philosophy (PhD) in Mathematics Education

Graduate Programs

The Ph.D. program emphasizes research and requires a written dissertation for completion. The program is individualized to meet the needs of graduate students. The student must develop, with the guidance from the major professor and committee, a program that is applicable to their background and interest. The average Ph.D. program requires 4-6 years beyond a master’s degree. The program is comprised of coursework in four major areas.

• Mathematics Education
• Mathematics or a related area
• Cognate Area
• Research Core

This residential program has rolling admission Applications must be fully complete and submitted (including all required materials) and all application fees paid prior to the deadline in order for applications to be considered and reviewed. For a list of all required materials for this program application, please see the “Admissions” section below.

• July 1 is the deadline for Fall applications.
• November 15 is the deadline for Spring applications.
• March 15 is the deadline for Summer applications.

This program does not lead to licensure in the state of Indiana or elsewhere. Contact the College of Education Office of Teacher Education and Licensure (OTEL) at [email protected] before continuing with program application if you have questions regarding licensure or contact your state Department of Education about how this program may translate to licensure in your state of residence.

APPLICATION PROCEDURE

Application Instructions for the Mathematics Education PhD program from the Office of Graduate Studies:

In addition to a submitted application (and any applicable application fees paid), all completed materials must be submitted by the application deadline in order for an application to be considered complete and forwarded on to faculty and the Purdue Graduate School for review.

Here are the materials required for this application:

• Transcripts (from all universities attended, including an earned bachelor’s degree from a college or university of recognized standing)
• Minimum undergraduate GPA of 3.0 on a 4.0 scale
• 3 Recommendations
• Academic Statement of Purpose
• Personal History Statement
• Writing Sample
• International Applicants must meet English Proficiency Requirements set by the Purdue Graduate School

We encourage prospective students to submit an application early, even if not all required materials are uploaded. Applications are not forwarded on for faculty review until all required materials are uploaded.

When submitting your application for this program, please select the following options:

• Select a Campus: Purdue West Lafayette (PWL)
• Select your proposed graduate major: Curriculum and Instruction
• Please select an Area of Interest: Mathematics Education
• Please select a Degree Objective: Doctor of Philosophy (PhD)
• Primary Course Delivery: Residential

Program Requirements

I. mathematics education courses (15 – 18 hours).

In mathematics education, students engage in courses that cover topics in the cognitive and cultural theories of learning and teaching mathematics, and the role of curriculum in mathematics education. A three (3) course sequence is required that consists of:

• EDCI 63500 – Goals and Content in Mathematics Education
• EDCI 63600 – The Learning of Mathematics: Insights and Issues
• EDCI 63700 – The Teaching of Mathematics: Insights and Issues

In addition, students are encouraged to take (6 – 9) hours of EDCI 620: Developing as a Mathematics Education Researcher

II. Related Course Work (minimum 6 hours)

All students should have appropriate course work in mathematics, statistics, educational technology, or a related field. Students without a master’s level background in mathematics may be required to take more courses in mathematics. This will be determined by the student’s major professor and advisory committee.

III. Cognate (9 hours)

Students will take three graduate courses in a self-selected cognate area. Cognate area selection should be discussed with the student’s major professor and advisory committee. Possible cognate areas include: mathematics, psychology, philosophy, sociology, technology.

IV. Research Core Courses (15 hours)

All doctoral students in the Department of Curriculum and Instruction must complete five (5) courses from areas in research methodology and analysis before beginning their dissertation:

• EDPS 53300 – Introduction to Research in Education
• EDCI 61500 – Qualitative Research Methods in Education
• MA 51200 – Introductory Statistics
• Advance electives in either quantitative or qualitative methods
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Mathematics Education PhD

Doctor of philosophy.

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Admissions Information

Displaying requirements for the Spring 2024, Summer 2024, and Fall 2024 terms.

• Points/Credits: 75
• Entry Terms: Spring/Summer/Fall

Application Deadlines

• Spring: November 15
• Summer/Fall (Priority): December 1
• Summer/Fall (Final): Rolling

* For details about rolling deadlines , visit our admission deadlines page.

Supplemental Application Requirements/Comments

• Online Degree Application , including Statement of Purpose and Resume
• Transcripts and/or Course-by-Course Evaluations for all Undergraduate/Graduate Coursework Completed
• Results from an accepted English Proficiency Exam (if applicable)
• $75 Application Fee
• Two (2) Letters of Recommendation

Requirements from the TC Catalog (AY 2023-2024)

Displaying catalog information for the Fall 2023, Spring 2024 and Summer 2024 terms.

View Full Catalog Listing

Doctoral Degrees

All candidates for the Ed.D., Ed.D.C.T., or Ph.D. degrees are expected to demonstrate both mathematics and mathematics education competencies through a series of certification examinations taken upon the completion of 60 graduate points. Certification examinations test the student’s knowledge of current research and theory in mathematics education and mathematics content. Examinations are offered once in the fall, spring, and summer terms. Courses recommended as preparation for the examinations in mathematics education include MSTM 6037,  MSTM 4019, and other mathematics education courses; Courses recommended as preparation for the examinations in mathematics are 6000- level mathematics content courses.

Students must demonstrate acceptable proficiency in at least three of the following six mathematics content areas: algebra, analysis, discrete mathematics, foundations of mathematics, geometry and topology, and probability and statistics. Students may sit for the examination in mathematics content during the regular certification examination times. Alternatively, they may register for advanced content courses and, with permission of the program, sit for the content area certification examination upon completion of the course. Incoming doctoral candidates should register for MSTM 6037 Professional Seminar in Mathematics during the first year of doctoral studies.

Doctoral students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Doctor of Philosophy in Mathematics Education

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree program requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Candidates are encouraged to develop an association with a faculty member early in their studies to identify a problem area of mutual interest to plan a course of studies that leads to the competencies needed to complete dissertation research and prepare for a professional role. Further details are available in the brochures on doctoral studies and in the general descriptions of doctoral programs available from the Office of Doctoral Studies (ODS).

A program of study for the Doctor of Philosophy degree must include at least 45 points taken under Teachers College registration. In order to permit the acquisition of broad and basic scholarship, each program of study should include at least 60 points in mathematics, mathematics education, statistics, and computing. At least 35 points should be in advanced courses – including research courses (MSTM 6500 or 6501 and MSTM 7500). (Any Teachers College course at the 6000 level or above, any Columbia University Graduate School of Arts and Sciences course with a “G” prefix, any “W” course numbered above 4000, or any transferred course with a graduate-level prerequisite will be considered an advanced course.) Further, 15 points in the philosophical, psychological, and curricular foundations of education must be included in every Ph.D. degree program. Students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Candidates for the Ph.D. degree are required to demonstrate competency in two languages chosen from among French, German, and Russian. Students who require other languages for the preparation of their dissertation may petition the program to request one substitution. Students in mathematics may not use computer languages or statistics to satisfy the language requirement.

The Ph.D. dissertation is a scholarly study contributing new theoretical knowledge to the field and should be planned early in the program when sufficient advanced courses have been completed to permit the candidate to enroll in relevant research courses. Ph.D. dissertations in mathematics education should be (1) experimental studies in learning, (2) analytical studies in policy theory in mathematics education, or (3) other scholarly investigations of problems and issues of broad significance in the field.

The website of the Program offers a list of Topic study groups which doctoral students are recommended to join.

• View Other Degrees

Program Director : Professor Alexander Karp

Teachers College, Columbia University 323 Thompson

Phone: (212) 678-3381 Fax: (212) 678-8319

Email: tcmath@tc.edu

The Graduate Program

The Department of Mathematics offers Ph.D. programs in Mathematics and Applied Mathematics. The department also supports students in the  Graduate Group in Logic and the Methodology of Science , an interdisciplinary doctoral program shared between the departments of Philosophy and Mathematics. At this time, we no longer offer a terminal Master's degree program.

To review the policies and procedures of the Graduate Program, please refer to our  Graduate Student Handbook .

Please note: Some Mathematics Advising Services have been moved to virtual platforms. You can find the latest information on UC Berkeley’s prevention and response efforts  related to COVID-19 here.

Graduate Program Contacts 

The Graduate Program is overseen by the Departmental Vice Chair for Graduate Affairs and the Graduate Student Affairs Officers. 

• Professor Tom Scanlon, Vice Chair for Graduate Affairs
• Clay Calder, Graduate Student Affairs Officer
• Christian Natividad, Graduate Student Affairs Officer 
• Vicky Lee, Director of Student Services

For Questions Regarding Math Graduate Admissions: Please see the Admissions web page  here . After reviewing the admissions website, if you have further questions please email [email protected] .

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This report presents a statistical profile of doctorates awarded by departments in the mathematical and statistical sciences at universities in the United States. Additional information was provided by the individual new doctoral recipients. Reports here are archival versions of reports published in Notices of the AMS . The archival reports incorporate corrections subsequent to publication, and they include tables on which the reports’ graphics and narrative are based.”

Master of Science in Mathematics and Applied Statistics

At California State University Long Beach

The Department of Mathematics & Statistics at CSULB offers four Master of Science programs .

Teaching & Graduate Assistantships provide students with funding and with college teaching experience.

Graduates have found employment in both technical and academic workplaces. Many have obtained tenure-track community college professorships. Others have gone on to PhD programs.

MS in Mathematics, General Option

Study and explore concepts in areas including analysis, algebra, topology, and geometry, as well as the   deep connections between and among these subjects.

MS in Mathematics, Option in Applied Mathematics

Study applied math methods with an emphasis on computational skills.

MS in Mathematics, Option in Mathematics Education for Secondary School Teachers

A flexible program that includes coursework in mathematics and in mathematics education research & theory.

MS in Applied Statistics

Using conceptual foundations and statistical software packages ( SAS , R , and Python ), students are trained to analyze real world data appropriately and communicate their findings effectively. The tools learnt here will open the door for careers in data science and analytics, or prepare you for a PhD in a variety of related fields.

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Dr. John Brevik, Pure Mathematics Graduate Advisor, [email protected]

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Dr. Kagba Suaray, Statistics Graduate Advisor, [email protected]

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Assistant Professor of Mathematics Education Samantha Marshall to Partner with Teachers to Improve Translanguaging Pedagogy through NSF CAREER Grant

In many mathematics classrooms, students are often seen as mathematically gifted if they can do things like perform quick computations, use specific mathematical terminology or complete math problems on their own. Assistant Professor of Mathematics Education Samantha Marshall says these criteria can often undervalue the skills multilingual learners bring to the mathematics classroom.

“For multilingual students, their multilingualism is often portrayed as a barrier to their learning when, in fact, it can be a significant resource for their sensemaking,” she said. “As one example, in many Latin American countries, the word used for one billion is “mil millones,” which translates literally to “a thousand millions.” In this example, a student’s language can provide conceptual resources for understanding mathematical ideas — especially this idea about the magnitude of one billion that many students struggle with.”

Marshall is now using a five-year, $926,102 National Science Foundation CAREER grant to partner with middle school teachers in order to co-design, analyze and improve teachers’ translanguaging pedagogies, or pedagogies that draw on students’ full linguistic repertoires as resources for learning. 

The project, entitled “Supporting Teachers to Leverage Students’ Languages in Mathematics,” will utilize three studies to investigate how teachers make sense of and enact translanguaging pedagogies, how translanguaging pedagogies shape students’ mathematical experiences and learning opportunities, and how teachers’ learning of translanguaging spaces can be supported. 

“In my prior work in the classroom, I have witnessed multilingual students being disciplined for not speaking loudly enough, speaking too loudly, not speaking with precisely the desired vocabulary or sentence structure, misunderstanding directions, speaking in their home language or asking for help,” Marshall said. “In all, there are so many levels at which multilingual students are marginalized in mathematics and that is one reason this project seeks to center the resources they bring, while also supporting teachers’ learning to leverage these resources.”

The first of the project’s three studies will see Marshall partner with teachers to co-design pedagogical resources, including lessons, mathematical tasks and pedagogical strategies to support translanguaging in middle school mathematics. These, Marshall said, will include strategies related to group work structures and whole-class discussion protocols.

In the second study, the project team will video record the co-designed translanguaging pedagogies as they are enacted in the classroom with a particular focus on the character of students’ learning opportunities and experiences. 

In the third study, video clubs will be created to support teachers’ learning about translanguaging pedagogies, using the videos filmed during the second study as a key learning resource. 

The video clubs, Marshall said, give educators an opportunity to analyze their practice with more time and space and the ability to pause, rewind and ask critical questions in a supportive teacher learning community. 

“Classroom video holds great potential to support mathematics teachers’ learning to leverage students’ languages because it opens a window into students’ learning experiences,” Marshall said. “By looking closely at how students’ languages become resources for mathematical sensemaking, teachers can begin to see not only a broader array of possibilities for translanguaging as a vehicle for mathematical understanding, but they may also gain important insights about how their own design, enactment and facilitation of translanguaging pedagogies allows students to capitalize on their linguistic resources for mathematical learning.”

The ultimate goal of the project is to end with a bank of co-designed translanguaging resources for middle school mathematics teachers and a bank of videos showing translanguaging pedagogies in action to guide teachers, teacher educators and researchers. Additionally, the project team aims to develop evidence about the character of students’ mathematical learning in translanguaging spaces and an empirically-grounded theory of teachers’ learning of translanguaging pedagogies. 

“I hope that both the practical and theoretical products inform the design of professional development and mathematics learning experiences for multilingual students, supporting nationwide efforts to improve mathematical access for students and redressing persistent opportunity gaps for STEM learning and access,” Marshall said. “Additionally, the project will directly contribute to the improved mathematical learning experiences of the 700 students taught by participating teachers each year. Ultimately, I hope that this project will help the field turn toward more asset-based forms of mathematics teaching and learning.”

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More From College of Education News

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100,000+ reasons why the Tech Equity partnership wants to help Nashville learn to code

Brian Kimbrow talks about learning code with the determination you’d expect from a former SEC running back.

It’s not easy. Far from it. 

Yet Kimbrow embraced months of technology training last year with CodeX Academy, taking time to learn something that at first read like a foreign language. 

And now, with support from a host of local business leaders, he’s inching closer to scoring a full-time gig as a full stack developer or software engineer. Expected entry-level salary: north of $100,000.

“If it’s something that you see that you want to achieve, accomplish, you can as long as you put your mind to it and remember that nothing is easy,” said Kimbrow, 31, a former student-athlete at Vanderbilt from 2012-15.

He's one of more than 500 CodeX Academy students, dating back to the program's launch in the fall of 2019. Then in January, he became a teacher's assistant, helping to guide the Tech Equity partnership's inaugural class of 34.

The Tech Equity partnership is supported by Amazon, the Tennessee Titans, Nashville Predators, Nashville Soccer Club, Vanderbilt University, Nashville State Community College and Tony Giarratana. These local employers connect with students hailing from underserved and underrepresented communities in North Nashville and Antioch, getting a first look at potential job candidates.

"Most companies will train and graduate — 'OK, good luck. Let us know how you do,'" said Phil Henry, the CEO of CodeX Academy. 

"We want to take it a step further and hold their hands throughout the entire process. To make sure they get proper, all-around training and help with soft skills that will help them get in the door."

The annual cost of the virtual program is $146,000, funded by a collection of local grants. 

"When schools, community organizations and for-profit entities work together to support learning, everyone benefits," said Stephanie Stanton, the senior DEI program manager for Community Engagement, Amazon Talent Acquisition. Stanton leads and manages Amazon’s partnership with CodeX Academy.

"Investing in the continued upskilling of residents creates a stronger workforce and also serves to keep the talent local."

Are tech jobs hiring in Nashville?

Software developer jobs are expected to be one of the most sought-after occupations during the next decade, according to the U.S. Bureau of Labor Statistics, with the growth rate increasing 26% between 2022-32. Meanwhile, jobs are estimated to demand a median pay of approximately $127,000 annually. 

Last year, the U.S. added 136,000 tech jobs.

While coding jobs are typically remote, some U.S. cities have become hubs for tech professionals. San Francisco/San Jose, Seattle, Denver, Austin, Boston and Washington D.C. top most lists, but Nashville's focus on healthcare, music and startups is increasing local opportunities.

Last year, Tennessee averaged more than 6,800 computer jobs each month with an average salary of $90,354, according to the 2023 State of Computer Science Education.

These Tennessee high school students are required to take a computer science class to graduate

In Tennessee, the Class of 2028 will mark the first group of public students required to take a computer science class to earn a high school diploma. Yet the state legislation has already made an impact.

More than 22,000 high school students took foundational computer science during the 2022-2023 school year, according to the 2023 State of Computer Science Education — nearly double the total of previous periods. And Tennessee is one of nine states where more middle school students were enrolled in computer science than high school students.

Is math required for tech jobs? Answers

Andrew Becker disapproves when adolescents say someone is naturally good at computer science. 

Hang on, he tells them, using himself as an example. He’s spent a lot of time in libraries; studying with peers; meeting with tutors; utilizing digital resources. An incremental journey from struggling to learning to thriving and much, much later, mastering. 

“Those advanced degrees didn’t come cheap,” joked Becker who teaches computer science at Antioch High. He was also the MNPS teacher last fall to work with Stanford University in a dual enrollment course which taught students the basics of computer science, along with coding and programming.

Count Becker as another professional who said mastering math is not the top prerequisite for a career in tech. Also, Computer Science Zone.org, which encourages careers in computer science and IT, lists the following attributes:

Self-reliance. Language. Logic.

Attention to detail. Recognition of stupidity. Abstract thinking. Patience. 

Strong memory. Scientific method. Communication and empathy.

No wonder Becker wants his students to embrace the journey, full of failures and setbacks.

"We don’t allow ourselves the ability to practice at math before we decide if we’re good or bad at it," he said. "We just say, 'Oh, I can do this, or I can't.' I have top students that take a (computer science) test — part of district testing. They can be scoring in the top of the class and not feel that they are. 

"Someone who thinks they're failing the class, but actually has some of the highest scores in the district."

Working in technology takes more than tech. After all, Henry wants his students to "wow" on interviews. That's why the Tech Equity partnership includes workforce readiness training, which helps students acquire soft skills that leave lasting impressions on hiring managers. 

Each participating company promises to support courses that prepare students with entry-level software development skills; serve as mentors and school ambassadors; offer job placement opportunities through business programs; and volunteer in-person and virtually.

"CodeX utilizes a top tier software development curriculum that teaches students the skills needed to be successful in tech roles," Stanton said. "More than that, they provide career preparation and soft-skills training resources to ensure students can navigate corporate spaces effectively inclusive of how to effectively communicate, how to elevate personal brand and how to discuss the impact of their work."

Sounds a lot like Kimbrow.

The Memphis native, who previously completed the technology training, is now matriculating through workforce readiness training. He's expected to wrap up this training around the time the inaugural Tech Equity partnership class graduates in September.

Henry expects the next Tech Equity partnership class of 50-70 students to start in January 2025.

Meanwhile, Kimbrow's career goal is to not just to enter the tech space, but create a running lane for others to rush through.

Gary Estwick is the business, race and culture editor at The Tennessean. Reach him at [email protected].