Should I Apply Straight to PhD's or a Master's first Given my Stats?

[Helpmepls]

Undergrad Institution: (No Name State School (very afraid of how much this will hurt me))
Major(s): Mathematics
Minor(s): Music
GPA: 3.98 (4.0 math)

GRE Revised General Test:
Q: 168
V: 165
W: 4.5

Graduate Level Courses by Graduation: Analysis I & II, Abstract Algebra I & II, Linear Algebra, Differential EQ I (maybe II)

Miscellaneous: Will attend Budapest Semester in mathematics this summer (plan to take a research course and complex analysis or something maybe), 2.5 years research experience with a paper prepared to submit to journals (got me selected to compete for Goldwater but did not win ) graduate level coursework by time of graduation:

For reference, I am a current junior, and I am very concerned that my application profile is not competitive enough to get into any of the Ph.D. programs I'm interested in at this point; I see many individuals on this site with upwards of 10 graduate level courses, and I'm working with only 6. Additionally, my parents made me attend a local college despite my ability to having gotten into some prestigious schools for undergrad: I think this also hurts my application significantly. Also everyone here seems to have at least a 169 on their Quant for GRE so I guess I'd better retake that. I'm wondering if I should just cut my losses and do a master's or try to do a Fullbright (hard to get I know) to make myself more competitive then do a Ph.D.

Target Schools: UPenn, Madison Wisconsin, University of Minnesota Twin Cities, University of Maryland College Park, Georgia Institute of Technology, Ohio State, Pennsylvania State University--University Park, NC Chapel Hill, Notre Dame, CUNY, University of Virginia, Dartmouth, Rensselaer (dream school)

Also I'm new here. Please forgive me if this kind of post is looked down on. I'm just looking for advice on what to do cause I feel like I'm fighting the current at the moment.

All in all, I hope someone can give me advice on what to do. Thank you.

[coolar]

You should apply to PhD programs. Don’t worry about retaking the GRE. Most schools don’t require it and the ones that do don’t really care. It is very much a “you must be this tall to ride this ride” type of thing. As long as you have decent scores, you will be fine. Make sure you have good letters of recommendation, as they will make or break your app when applying to competitive schools because most people’s apps will be very similar.

[Jmr324]

This post is ridiculous. Have you ever looked at the profiles on this forum? MANY people with similar stats get into the programs you listed. You have a great GPA, multiple graduate-level courses, research experience (that will result in a paper). Assuming your letters are good, the only downside of your app is you don't go to a prestigious school, but many people get into good schools from unknown state schools. Give me a break, lol.

[Helpmepls]

This post is ridiculous. Have you ever looked at the profiles on this forum? MANY people with similar stats get into the programs you listed. You have a great GPA, multiple graduate-level courses, research experience (that will result in a paper). Assuming your letters are good, the only downside of your app is you don't go to a prestigious school, but many people get into good schools from unknown state schools. Give me a break, lol.

Hi, apologies if I'm being ridiculous; however, I was looking through profiles today in the yearly forums, and I was like "oh no these people are being rejected from my target schools with like twice the amount of grad courses as me and higher test scores what am I gonna do?" So honestly, I appreciate the feedback.

[clopensets]

I know the seeing people applying now getting rejections can be stressful. However, there is inevitably going to be random chance involved in any admissions cycle. It's just that competitive. I got rejected from 10 schools last year and now I am admitted to 3 programs. You have an extremely competitive profile, stronger than mine. You really should go for the PhD.

[Jmr324]

This post is ridiculous. Have you ever looked at the profiles on this forum? MANY people with similar stats get into the programs you listed. You have a great GPA, multiple graduate-level courses, research experience (that will result in a paper). Assuming your letters are good, the only downside of your app is you don't go to a prestigious school, but many people get into good schools from unknown state schools. Give me a break, lol.

Hi, apologies if I'm being ridiculous; however, I was looking through profiles today in the yearly forums, and I was like "oh no these people are being rejected from my target schools with like twice the amount of grad courses as me and higher test scores what am I gonna do?" So honestly, I appreciate the feedback.

If you have strong letters of rec, you will be fine. Ask your letter writers for some schools they think you would be competitive at.

[LetMeIn2401]

How is linear algebra a grad level class.