1. I failed PHYS1003. Sydney uni doesn't have it in summer/winter school so I have to do it next year, therefore make my graduation longer. Is it possible to do it in other uni? (UNSW has the same subject in the summer this year), or is there another option so that my graduation won't be 1 year longer?
I don't think doing at UNSW would be an option. I have a friend at UNSW doing Physics 1B at Summer School, and they are already into their second week. So, you can overload, as mentioned before, however, with careful planning you can complete your degree within your allotted time frame without overloading.
Here's what I'd recommend:
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Firstly, you have four subjects that you need to do next semester; COMP2129, ELEC1103, ELEC2602 and MATH2061.
Do MATH2061 at Summer School (enrol as soon as you can). This will free up your timetable for my further recommendations.
Now, fortunately for you, the only unit in your degree that you need PHYS1003 as a prerequisite for is PHYS2213 (Physics 2EE). PHYS2213 is offered in Semester 2, and of course, you can't do them both at the same time. So
do PHYS1003 again in Semester 2 next year, and do PHYS2213 in Semester 2 during your third year. PHYS2213 is not a prerequisite for any other units in your degree, so you won't be holding yourself back by doing the unit a year late.
So when you get to third year, you'll have a number of electives available to you. There are 9 core units listed in the handbook, of which you have to do at least 5. There are also a number of electives, labelled ELEC4XXX and ELEC5XXX, however, the department classifies these as advanced units of study, so you do not have to do them if you want, and you can take as many of the normal level core units as you want to make up for those electives. But don't worry, you have a bit of time before you need to choose your electives.
I would do one of these core units in place of MATH2061 for next semester, my recommendation would be ELEC3404 (Electronic Circuit Design). A lot of the core units are quite loose on their prerequisites, and I think ELEC3404 is the loosest of them all; all they assume is that you have a basic knowledge of electronics and circuit theory. So hopefully you won't have too much trouble with that subject. Then just pick the rest of your third year electives when the time comes and you'll be sweet.
So short summary: Do MATH2061 at Summer School, do your second year units replacing MATH2061 with ELEC3404 and PHYS2213 with PHYS1003, and do PHYS2213 Semester 2 of your third year. Do your third year electives and fourth year honours/project, and you should have completed all requirements for your degree, in four years as required
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2. Is it true that for Engineering (I am doing electrical engineering), students need to finish their study maximum in 5 years in order to get into Honour program in their final years?
I transferred from civil last year, and doing electrical engineering start from this year, therefore I need minimum 5 years in total (civil 1 year + electrical engineering 4 years, because civil and electrical have different set of subjects for first year), but because I failed PHYS1003, I need minimum 6 years to finish my degree
The fourth year of your engineering degree is your honours year (or project year if you are doing a pass degree). So by my count, by that stage you would have only completed 1 year of civil and 3 years of electrical. So you should be fine to do honours if you wish provided your marks are good enough.