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My story revolves about a life of a girl that is profoundly gifted even among a family of profoundly gifted. Her father founded a multi-billion dollar company focused on IT security and cryptography when he was a teenager, which made him very wealthy. Her mother is a professor at a prestigious university,and her older siblings are also profoundly gifted, all of them skipped several years.

While normal 7 year old children are starting their first grade at elementary school, she applies to a Master degree Applied and Computational Mathematics. While the dean and rest of a admission board are impressed with her knowledge of Stochastic Processes and Mathematical Optimization they are only ready to accept her as an undergraduate student to fill the holes in the subjects she previously found unimportant.

Would a US university accept a 7 year old, who is already over-prepared for college if she doesn't have any formal education?

The point is that she never had any formal schooling in her whole life. Since in the age where she needs to enter the system she is already college degree ready.

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closed as off-topic by elemtilas, Renan, JohnWDailey, Shadowzee, user535733 Dec 14 '18 at 2:21

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about worldbuilding, within the scope defined in the help center." – Renan, JohnWDailey
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Many nations have an aptitude test that can be undertaken for university admissions if an individual lacks the common entry requirements. For example, if your schooling was in a different nation and the university is therefore unable to use your high school results. $\endgroup$ – Arkenstein XII Dec 13 '18 at 22:51
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    $\begingroup$ AFAIK, in the U.S. of A. many universities are actually private enterprises, operating either for-profit or on a not-for-profit basis. As private enterprises they may accept whomever they please in whatever role they please. However, I would expect that accepting a seven year old child as a student would hit the snag that the seven year old child has the ethics and social skills of a seven year old child, that is, none whatsoever. $\endgroup$ – AlexP Dec 13 '18 at 23:08
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    $\begingroup$ So many issues here! First of all, welcome to Worldbuilding Stack Exchange! Please take a moment to review the help center and tour. They will give you a good idea as to what kinds of questions are allowed here. First, your question is not about worldbuilding. It is about real world uni entrance policies. Therefore off topic. Second, you obviously did not do any prior research whatsoever. 2 seconds on google will show you many instances of young children attending and graduating uni. Third, your question is really probably more about the plot of your story, which is off topic here. VTC. $\endgroup$ – elemtilas Dec 13 '18 at 23:25
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    $\begingroup$ I'm voting to close this question as off-topic because No prior research: google answers this question right away. $\endgroup$ – elemtilas Dec 13 '18 at 23:26
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    $\begingroup$ @AlexP I don't think that would matter much considering that her father is a billionaire and the school would probably welcome the publicity. Also, any child that gifted that I have ever heard of is often more mature than expected for their age out of the simple fact that they are smarter. Not necessarily adult level gifted, but enough to function in a semi-professional capacity. $\endgroup$ – TitaniumTurtle Dec 14 '18 at 0:27
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Lots of people go to college after being homeschooled (with no brick and mortar schooling at all). Even unschooling (where the parent doesn't do anything formal, just gives the child opportunities and allows them to choose what to learn) is enough to prepare a child for college.

After all, many of the top colleges were founded back when only the wealthy had higher education (or much education at all) and it was common for children to have tutors at home (later, boarding schools for teens and sometimes younger children were also common).

From a simple Google Search, I came up with dozens of links right away. Here are a few excerpts.

The Homeschooler’s Guide to Getting Into College

Top schools including Harvard, MIT, Duke, Yale, and Stanford are all actively recruiting homeschoolers. These schools don't just grudgingly accept homeschooled students, they do everything they can to get them in the door, recognizing that homeschoolers are often better prepared for college than their brick-and-mortar schooled peers.

Can Homeschoolers Attend College?

Colleges are aware that homeschoolers do not fit the typical student mold and understand that the components of their application may look different. Admissions departments are very helpful, and some colleges (ranging from Princeton to Biola) have even set up special pages for homeschooled applicants.

How Do Colleges Evaluate Homeschooled Students?

Home schooled students looking to attend competitive universities should take particular care in preparing for their standardized tests, because test scores are one of the few ways in which admissions committees can compare them to other students academically...Comparison to similar students is one of the primary ways admissions committees weigh the significance of an individual student’s accomplishments, which makes evaluating home schooled students particularly tricky. Regardless of the rigor of a student’s course load, colleges cannot determine academic achievement using grades alone.

Age is certainly a factor and no college is going to take a small child just because she is brilliant. She has to have a well-rounded education, regardless of the source. Tim B has given some good examples where age is not a dealbreaker.

So, yes, it would be quite rare but possible. Especially in a case where the university might make a specialized curriculum for such a child (to appease the parents and get the donations).

Note: While Universities and Colleges are not quite the same thing, in the U.S. we often use the terms interchangeably.

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    $\begingroup$ "... no college is going to take a small child just because she is brilliant. " I disagree. All it takes is one psychology professor who convinces the college to admit her as a long-term psych project, with him being the guarantor of her behavior, and it could certainly happen - especially in a world with lower ethical barriers to experimenting on people. $\endgroup$ – Laughing Vergil Dec 14 '18 at 1:04
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    $\begingroup$ @LaughingVergil And you just gave a reason other than brilliance. The chance to experiment on her. Another reason might be money. My point is that brilliance in and of itself isn't enough. Either the child has to be ready for the academic challenge or the university has to be getting something out of it. $\endgroup$ – Cyn Dec 14 '18 at 1:24
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In which country?

There are numerous reported cases of children entering university young. They just need to prove to the university that they are a suitable candidate. The usual way to do that is formal education and grades in prior subjects but that is far from the only way.

For example:

These articles don't say what prior qualifications these candidates have but it gives you some idea what is possible. You can find plenty more examples by searching.

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