Be polite and friendly to her, while respecting her choice. Don't stop being her friend. If things do go wrong, she'll remember that you remained friendly and respectful and she may just come to you in a time of need. Don't do anything to break them up, it's too risky and it's better to let things take their course.
Look at her, not stare, just look. When she looks at you, smile a bit, not too happily from ear to ear. If she smiles back, you can approach her. Nothing ventured, nothing gained.
Keep talking and ask her leading questions; finding a topic she is interested in and comfortable with will help immensely. Lastly, remember to respect her interest and privacy.
Try leaving noticeable but humble clues, but don't become invasive. For example, ask what her favorite color is, what she hopes to do with her life, where she would love most to travel in the world, etc. Then remember what she tells you and be sure to raise conversations about those topics or create something based on those things to surprise her, such as a travel dream journal or make her a bracelet in her favorite color. These things will impress her.
You could tell her that you fancy her and show her what she means to you. But don't keep asking or moan at her choice! If she says no, then she's not the one for you. However, if you don't ask her, you won't know if she happens to feel the same way about you. Since you've never told her, she may not think you like her. So asking her would be a good choice. And play it calm! Become friends. As your friendship goes deeper, she may come to realize that she likes you better. Focus most on being her friend above all else and let time do the rest.
Tell her that you love her, that she is an important presence in your life and that you're happy to wait until she changes her mind. Then accept her friendship. It may take time but the fact that you didn't push her, didn't throw a tantrum and didn't neglect her but instead respected her decision and still offered love, will weigh heavily in her mind and will, as the article is all about, impress her.
If you want to be nice to her and not make fun of her, find a mutual interest or hobby. If she sees or hears something about the subject and she wants to talk about it, she'll come to you first, because you know your stuff. Also, hold the door open for her and if she has a problem, try everything you can to solve it with her, not for her, but with her. She'll see you as the interesting problem solver instead of the macho guy who likes himself more then he likes her.
Analyze the relationship she is already in. If you think you can be a better partner to her, then there's no harm in simply trying to impress her. She can make up her own mind about it.
Try to get accepted by the group as an okay guy. After the group knows and likes you, you'll be able to try to get closer to her. This may take time, so focus on this being there for a time.
You just feel it. And along with it, your partner too will.
Try to keep it simple, you don't want to overdress. Otherwise he might think you spend too much time on your appearance.
Smile back at him if you like him and see what happens from there!
Take the initiative to speak and interact with him as much as possible. He will be able to get over his shyness only if you can show him (maybe after a long period of time) that you are a non-threatening, kind person of whom he does not have to be afraid.
Gradually start to grow your relationship, start talking more, then high fiving or hugging, take a picture and have him put his arm around you, and just be yourself.
That might mean he's interested in you or that he's not that close to you -- it could go both ways, so it depends on the context. However, it does seem to indicate that he feels a romantic inclination rather than a brotherly one toward you...
You shouldn't even try, if a boy doesn't accept you, then you don't need him. You should never feel pressured to impress a boy; you are absolutely fine the way you are.
Make him feel good about himself, and allow him to open up a bit by asking him questions about his interests.
Continue to be yourself, and see what happens.
A simple yes and a smile if you are interested, or a kindly phrased let down will if you are not.
If he likes the studies, too. You could casually bring it up and see what his opinions are.