Program Recommendations

[ilovemath69420]

Good morning! I'm graduating in the spring, and am looking to get a PhD in Pure Math, maybe with a focus in abstract algebra, number theory, or analysis. Here's my experience:

School: Small state school in the south
Majors: Math: General + Computer Science: Software Systems
GPA: (Overall) 3.76 (Math) 3.92 (CPSC) 3.65
GRE: Didn't take
(Relevant) Coursework: Abstract Algebra, Analysis, Number Theory, Numerical Analysis, Geometry, Linear Algebra, Calculus of Variations, Analysis II, Topology
Research Experience:

• Undergraduate Research Assistant studying Knot Theory (March 2022- July 2022)
• Senior Capstone Research Paper on Pythagorean Triples (Spring 2023)
• Optional Senior Research Project on Quantum Mechanics (Fall 2023-Present)
• Attended Weekly Research Colloquiums (Spring 2023-Present)

Awards:

• Math Department Senior Award
• Full Ride Scholarship to school from Math Department

Clubs:

• Math Club: Founder + President (Fall 2022-Present)
• Pi Mu Epsilon: President (Fall 2022-Present)
• Film Club: President (Summer 2023-Present)

Job Experience:

• Math Plaza Tutor (Fall 2021-Present)
• Calc I Teaching Assistant (Fall 2022)
• Calc II Teaching Assistant (Fall 2021)
• Calc III Teaching Assistant (Spring 2022-Present)
• Linear Algebra Teaching Assistant (Spring 2023-Present)
• Math 1010 Tutor (Fall 2023-Present)
• College of Engineering and Computer Science Ambassador (Fall 2023-Present)
• Computer Science + Engineering Peer Tutor (Fall 2022-Present) (Tutored for Intro to Operating Systems, Advanced Data Structures + Algorithms, Software Design + Development, Digital Logic + Intro to Computer Hardware, and Computer Architecture)
• Not sure if this is relevant, but: Journey's (May 2021-August 2021); Gamestop (June 2022-January 2023)

Programming Languages: Java, HTML/PHP, Python, MATLAB, LaTeX, R, SQL
My recommendation letters are all strong, 1 coming from the department head, 1 coming from a professor I TA for + am doing research with + taking graduate level class from, 1 coming from my Analysis and Geometry professor.

Here's the schools I'm considering applying to: Duke, UPenn, Johns Hopkins, Rice, UNC Chapel Hill, Notre Dame, UVA, UGA, University of Tennessee Knoxville, University of Delaware, Clemson, Colorado State, University of Alabama, University of New Mexico, University of Vermont

Am I overestimating my abilities? Should I consider any other programs? If anyone could share their thoughts, that would be amazing.