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Mathematics - phd, admission requirements.

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For the 2024-2025 academic year

See 2025-2026 requirements instead

Fall 2024 quarter (beginning in September)

Priority deadline: February 1, 2024

Final submission deadline: June 3, 2024

Winter 2025 quarter (beginning in January)

Final submission deadline: November 15, 2024

International submission deadline: September 9, 2024

Priority deadline: Applications will be considered after the Priority deadline provided space is available.

Final submission deadline: Applicants cannot submit applications after the final submission deadline.

Degrees and GPA Requirements

Bachelors degree: All graduate applicants must hold an earned baccalaureate from a regionally accredited college or university or the recognized equivalent from an international institution.

University GPA requirement: The minimum grade point average for admission consideration for graduate study at the University of Denver must meet one of the following criteria:

A cumulative 2.5 on a 4.0 scale for the baccalaureate degree.

A cumulative 2.5 on a 4.0 scale for the last 60 semester credits or 90 quarter credits (approximately two years of work) for the baccalaureate degree.

An earned master’s degree or higher from a regionally accredited institution or the recognized equivalent from an international institution supersedes the minimum GPA requirement for the baccalaureate.

A cumulative GPA of 3.0 on a 4.0 scale for all graduate coursework completed for applicants who have not earned a master’s degree or higher.

Program GPA requirement: 2.5 on a 4.0 scale

Official scores from the Test of English as a Foreign Language (TOEFL), International English Language Testing System (IELTS), C1 Advanced or Duolingo English Test are required of all graduate applicants, regardless of citizenship status, whose native language is not English or who have been educated in countries where English is not the native language. Your TOEFL/IELTS/C1 Advanced/Duolingo English Test scores are valid for two years from the test date.

The minimum TOEFL/IELTS/C1 Advanced/Duolingo English Test score requirements for this degree program are:

Minimum TOEFL Score (Internet-based test): 80

Minimum IELTS Score: 6.5

Minimum C1 Advanced Score: 176

Minimum Duolingo English Test Score: 115

Additional Information:

Read the English Language Proficiency policy for more details.

Read the Required Tests for GTA Eligibility policy for more details.

Per Student & Exchange Visitor Program (SEVP) regulation, international applicants must meet all standards for admission before an I-20 or DS-2019 is issued, [per U.S. Federal Register: 8 CFR § 214.3(k)] or is academically eligible for admission and is admitted [per 22 C.F.R. §62]. Read the Additional Standards For International Applicants policy for more details.

Application Materials

Transcripts, standardized test scores, letters of recommendation.

Required Essays and Statements

We require a scanned copy of your transcripts from every college or university you have attended. Scanned copies must be clearly legible and sized to print on standard 8½-by-11-inch paper. Transcripts that do not show degrees awarded must also be accompanied by a scanned copy of the diploma or degree certificate. If your academic transcripts were issued in a language other than English, both the original documents and certified English translations are required.

Transcripts and proof of degree documents for postsecondary degrees earned from institutions outside of the United States will be released to a third-party international credential evaluator to assess U.S. education system equivalencies. Beginning July 2023, a non-refundable fee for this service will be required before the application is processed.

Upon admission to the University of Denver, official transcripts will be required from each institution attended.

GRE scores are optional for admission to this program. Applications submitted without scores will receive full consideration. Every application undergoes a comprehensive evaluation, including a careful review of all application materials. If you choose to submit test scores, you may upload your Test Taker Score Report PDF, which is considered unofficial. Official scores must be received directly from the appropriate testing agency upon admission to the University of Denver. The ETS institution code to submit GRE scores to the University of Denver is 4842.

University Standardized Test Policy

Three (3) letters of recommendation are required.  Letters should be submitted by recommenders through the online application.

Essays and Statements

Personal statement instructions.

A personal statement of at least 300 words is required. The statement should include information concerning your life, education, practical experience, special interests and specific purpose in applying to the University of Denver’s Department of Mathematics.

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Your submitted materials will be reviewed once all materials and application fees have been received.

Our program can only consider your application for admission if our Office of Graduate Education has received all your online materials and supplemental materials by our application deadline.

Application Fee: $65.00 Application Fee

International Degree Evaluation Fee: $50.00 Evaluation Fee for degrees (bachelor's or higher) earned from institutions outside the United States.

Applicants should complete their Free Application for Federal Student Aid (FAFSA) by February 15. Visit the Office of Financial Aid for additional information.

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PhD students resources

This page houses various resources for PhD students.

The PhD in mathematics degree requires:

• completion of at least 135 graduate-level credits beyond the BA or BS degree;
• passing of preliminary examinations;
• completion of a tool requirement;
• and completion of a written dissertation.

Although a master’s degree is not a prerequisite for acceptance into the PhD program, each student is required to obtain a master’s degree in mathematics before completing 80 credits in the PhD program.

Course Requirements

Of the 135 credits, a minimum of 36 credits of MATH courses must be completed at the 4000 level. Up to 35 credits may be taken in other relevant disciplines, as approved by the mathematics department graduate committee. Courses should be chosen in consultation with the student’s academic advisor.

• Mathematics course catalogue

Preliminary Examinations

The preliminary exams in algebra and analysis take place two times every academic year, typically during the week immediately preceding the beginning of the fall quarter and during the first week of the winter quarter.

All students admitted to the PhD program must pass preliminary exams in algebra and analysis by the end of the winter quarter of their second year of study. The following documents govern this requirement.

• Preliminary exam requirements
• Syllabus for algebra preliminary exam
• Syllabus for analysis preliminary exam

Some past, sample exams:

• Algebra prelim, Fall 2015
• Analysis prelim, Fall 2015
• Analysis prelim, Fall 2013
• Algebra prelim, Fall 2014
• Analysis prelim, Winter 2013
• Algebra prelim, Fall 2012
• Analysis prelim, Fall 2012
• Algebra prelim, Fall 2011
• Analysis prelim, Fall 2011

Tool requirement

It is strongly recommended that students satisfy their tool requirement by demonstrating the ability to use a modern computer typesetting system. Other options include:

• reading competency in two languages selected from French, German and Russian,
• a series of outside courses in another discipline,
• a significant laboratory experience involving mathematics.

Dissertation

The dissertation must make a significant contribution to the research literature in mathematics.

After the dissertation has been completed, the student must defend it in a final examination, as specified by the Office of Graduate Studies.

Please refer to the Office of Graduate Education manual for  thesis and dissertation formatting guidelines .

Transfer credits

The Department of Mathematics adheres to standard transfer credit policy outlined by the Office of Graduate Studies. (See  Graduate Policy Manual , p. 51-52)

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The Common App is a universal application that can be sent to many schools, including the University of Denver.

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Go to the graduate admission application to submit your information. For information on admission requirements, visit the graduate academic programs page and locate your program of interest.

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Information Bulletin of UG DUET - 2020-21: English --> https://pgcuet.samarth.ac.in/ --> College-Program wise preference count - CSAS 2022 | Common Seat Allocation System 2022 | Schedule of CSAS Round III

For undergraduate admissions register at cuet.samarth.ac.in | for postgraduate admissions register at pgadmission.uod.ac.in/ -->, ph.d. admissions.

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PhD Entrance Exam Syllabus

Rohini Pandey ,

Mar 4, 2024

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Here you will find everything about the PhD Entrance examination syllabus for various universities in India.

Table of Contents

List of Top PhD Streams and Courses

Top phd courses wise syllabus, phd entrance exam eligibility, du phd entrance exam syllabus, jnu phd entrance exam syllabus, mlsu phd entrance exam syllabus, phd entrance exam pattern.

The Doctrine of Philosophy (or PhD, for short, and 'Doctrine' in more social occasions) courses are considered to be the highest grade of courses made available in India. They're offered in various fields and disciplines, which includes all three streams of science, commerce, arts. The nature of obtaining a PhD requires you to be highly research-oriented since the work itself is similar. Candidates have to submit their final thesis on the subject they chose to pursue. This thesis, in return, must be based on the research done in that particular field and provide a satisfying, logical conclusion.

PhD courses are offered in various streams and with multiple courses for some of them. The entire list of PhD streams and the popular courses are mentioned in the table below:

PhD syllabus varies for each course, there is a wide range of scope for each candidate. However, the entire list of PhD syllabus along with their streams are tabulated in the table below:

Obtaining a PhD showcases the candidate's excellence on the field of their choice. The research projects and theses they submit are testament to what new practices and conventions they can bring to the field. Alternatively, they can project the knowledge they have to the younger generation through their positions as academic professors or lecturers in the best colleges offering PhD courses.

Since a PhD means you're the best in the field, you'll obviously be placed in higher positions in any organisation that does work under that particular field. Fellowship programmes can be headed by you. Lectures and  you will also be offered professor post in many of the universities, and a lot of fellowship programs also make the candidates complete their fellowships by giving lectures to the university students of the courses that the candidate is doing the fellowship in.

The eligibility for this course involves a postgraduate degree with a minimum score set by the university you're interested in. The core subjects of the postgraduate degree will be considered as the eligible fields in which the candidate can pursue their PhD programme. Even though some of the colleges offer admissions based on merit in their postgraduate degrees, most universities conduct their own entrance exams as a gateway to their PhD courses.

The syllabus for the exams is generalised for all candidates, and is largely aptitude-based. Depending on the course and the feasibility, some universities conduct the appropriate exam. With that out of the way, here's a look at the syllabus of the most famous entrance exams for PhD admissions.

Delhi University is one of the top universities of the country; it has 700+ college-based affiliations, centres across the most popular states, the largest student population in Asia, and is one of the largest universities in the world. Delhi University offers admission to various PhD programs based on the score, which the candidate achieved in the entrance exam. Some colleges under Delhi University offer admissions to PhD courses based on the merit you've obtained in any postgraduate course. Here's how the PhD entrance exam syllabus and the exam pattern works, after which we'll also take a look at the courses:

• Quantitative Methods For Research: There will be 60 questions in this section.
• Accounting Finance and Tax: There will be 35 questions in this section.
• International Business and Marketing: There will be 35 questions in this section.
• HRM and Law: There will be 35 questions in this section.
• Economics: There will be 35 questions in this section.

DU PhD Courses Offered

Jawaharlal Nehru University is located in New Delhi, and is also considered to be one of the largest universities of the country. Its influence spreads across 3 states: Delhi, Uttar Pradesh, and Haryana. This is thanks to the innumerable affiliations to other colleges and universities. The university offers more than 200 courses under UG, PG, and PhD Courses, and annually conducts entrance exams as a way to obtain admissions to various PhD programmes and courses.

Their PhD entrance exams are largely MCQ-heavy, with questions on PG-level mathematics, statistics, computer science and general aptitude. Here is the appropriate JNU PhD entrance exam syllabus:

Mohanlal Sukhadia University (MLSU) is considered to be one of the best universities in Udaipur, Rajasthan. It's is a state-governed university established to cater to the educational needs of candidates living in Udaipur and its surrounding areas. The university offers more than 200 courses to all the aspiring candidates across the nation.

It offers admissions to various courses that extend to its affiliated colleges via annual entrance exams. Admissions are offered based on the score of the candidate in these exams. But that's easier said than done because due to its reputation, you'll face strong competition in the exams. Here's their syllabus:

• The 1st paper consists of general topics.
• The 2nd paper consists of questions based on the specialisation you chose.
• Both papers have 100 as its total score.
• General topics consist of PG-level aptitude and general awareness questions, presented in an MCQ format. You have to choose between 4 options in the questions provided.
• The core paper consists of PG-level questions in the subjects you chose.
• You're also required to cover both the MCQ and descriptive questions on the paper.
• Some of those questions are research-oriented so as to test your research skills. It also gives you an idea of how the course works, and what you could expect from it.

As we already know, PhD is pursued by candidates who want to excel in their field of specialization. The entrance exam is expected to be tougher than any other exam. Commonly, the questions are based on the paper of specialization. The traditional PhD exam patterns are as follows:

• The exam is conducted both online and offline, depending on the particular conducting authority.
• The questions are mainly in MCQ patterns. 
• Usually, Part A consists of research questions in numerical ability, language proficiency and logical reasoning.
• Part B consists of technical questions related to the specific discipline.
• For each incorrect answer, marks will be deducted. 
• The duration and the number of questions vary for each PhD entrance exam. 
• Additionally, the exam pattern may vary depending on the conducting authority. 

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Master of Science

Programme overview.

The two-year master programme in Mathematics has been the department’s flagship teaching programme, since its inception in 1947. On an average, about 450 students secure admission to this programme every year across the North and the South Campuses. The course has been designed in a manner so that the students gain an in-depth knowledge of a broad range of topics and produce students with a good-firm background in both theoretical and applied mathematics. 

The programme comprises of 18 courses to be taught over 4 semesters and in 2 years. In the first two semesters, the focus is on core courses. In the last two semesters, the students have the option to choose courses from a pool of choices. In total, the students have to do eight elective courses along with two open elective courses in the third and fourth semesters. The curriculum of the programme has evolved continuously in tune with the changing contours of the discipline with recent advances.

Structure of the Programme

Beginning the academic year, the following courses are taught:

Each core and elective (open elective) course will carry 100 (50) marks and have two components: Internal Assessment 30 (15) marks and End-Semester Examination 70 (35) marks.

Guidelines for the Award of Internal Assessment Marks

30 (15) marks are allocated for Internal Assessment in each Core and Elective (Open Elective offered by the Department of Mathematics) paper. Of this, 20 (10) marks will be based on in-house examinations, with a common question paper across sections, while 10 (5) marks are for evaluation by individual teachers in each Core and Elective (Open Elective offered by the Department of Mathematics) paper. This evaluation may be done by the teacher via class tests, assignments, presentations, viva-voce etc.

66% attendance in lectures required to appear for the end semester examination while 50% attendance for the in-house examination. Students availing medical leave are required to submit the medical certificate to the concerned teacher within a week of joining back after availing the medical leave.

Department of Mathematics

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